# Algebra - Simplifying Algebraic Fractions

a - answer    s - solution    v - video

## Question 1

Simplify

a) $\dfrac{6x}{4}$a s v
b) $\dfrac{8x}{6}$a s v
c) $\dfrac{8x}{10}$a s v
d) $\dfrac{21x^2}{14}$a s v
e) $\dfrac{46y}{2}$a s v
f) $\dfrac{9\sqrt{a}}{27}$a s v

## Question 2

Simplify

a) $\dfrac{15}{10x}$a s v
b) $\dfrac{40}{30y}$a s v
c) $\dfrac{16}{4p}$a s v
d) $\dfrac{48}{20a^3}$a s v
e) $\dfrac{9}{14h}$a s v
f) $\dfrac{36}{32m}$a s v

## Question 3

Simplify

a) $\dfrac{2y}{3y}$a s v
b) $\dfrac{10x}{4x}$a s v
c) $\dfrac{15z}{5z}$a s v
d) $\dfrac{5x^2}{5x^2}$a s v
e) $\dfrac{2\sqrt{y}}{7\sqrt{y}}$a s v
f) $\dfrac{48y^5}{36y^5}$a s v

## Question 4

Simplify

a) $\dfrac{3x^2}{2x}$a s v
b) $\dfrac{9p^3}{5p}$a s v
c) $\dfrac{5y^2}{y}$a s v
d) $\dfrac{16z^5}{12z^2}$a s v
e) $\dfrac{21q^8}{35q^3}$a s v
f) $\dfrac{44c^{12}}{20c^{12}}$a s v

## Question 5

Simplify

a) $\dfrac{4x}{5x^3}$a s v
b) $\dfrac{8x^2}{6x^5}$a s v
c) $\dfrac{9v^3}{15v^3}$a s v
d) $\dfrac{35y^4}{50y^{17}}$a s v
e) $\dfrac{42a^4}{24a^5}$a s v
f) $\dfrac{19t^{13}}{3t^{13}}$a s v

## Question 6

Simplify

a) $\dfrac{2(x+1)}{3(x+1)}$a s v
b) $\dfrac{18(y-2)}{6(y-2)}$a s v
c) $\dfrac{22(x^2+4)}{10(x+1)}$a s v
d) $\dfrac{15(x-1)}{39(x-1)^2}$a s v
e) $\dfrac{77(2x+3)^3}{44(2x+3)}$a s v
f) $\dfrac{8(4z^2+5)^8}{11(4z^2+5)^{10}}$a s v

## Question 7

Simplify

a) $\dfrac{x^2y}{x}$a s v
b) $\dfrac{4xy^7}{xy^2}$a s v
c) $\dfrac{20x^4y^2}{15x^3}$a s v
d) $\dfrac{10a^6}{25a^2b^5}$a s v
e) $\dfrac{4x(x+5)}{3(x+5)}$a s v
f) $\dfrac{48h^2(g-3)}{40h}$a s v

## Question 8

Simplify. Leave answers with positive indices

a) $\dfrac{5x}{x^{-2}y}$a s v
b) $\dfrac{4y^{-3}}{xy}$a s v
c) $\dfrac{2x^{-5}y^{-3}}{10x^{-1}y^{-2}}$a s v
d) $\dfrac{15a^{-2}b^{-5}}{6a^{-6}bc^{-1}}$a s v
e) $\dfrac{21x^{-3}y^4z}{56x^{-8}y^{-1}z^3}$a s v
f) $\dfrac{108m^{-9}npq^{-15}}{60m^{-2}n^{-12}p^5}$a s v

## Question 9

Simplify. Leave answers with positive indices

a) $\dfrac{-4a^2bc}{2ab^2}$a s v
b) $\dfrac{10xy^3}{-6xyz}$a s v
c) $\dfrac{-8p^3q^2r}{-20pq^2r^3}$a s v
d) $\dfrac{45p^{-2}q^4}{25p^7q^{-1}}$a s v
e) $\dfrac{33c^{-1}d^{-7}e}{-21c^{-1}d^3e^8}$a s v
f) $\dfrac{-27w^{-3}x^{14}y^{-9}z}{-63w^2x^{-3}z^{15}}$a s v

## Question 10

Factorise and simplify

a) $\dfrac{6x+4}{4}$a s v
b) $\dfrac{8p-14}{2}$a s v
c) $\dfrac{15w+35}{20}$a s v
d) $\dfrac{21a-30}{12}$a s v
e) $\dfrac{18a^2-20a}{14a}$a s v
f) $\dfrac{42g^2-66g^5}{24g^3}$a s v

## Question 11

Factorise and simplify

a) $\dfrac{4x+8}{6x+12}$a s v
b) $\dfrac{9x+3}{3x+1}$a s v
c) $\dfrac{x^2+3x}{2x+6}$a s v
d) $\dfrac{xy-2y}{4x-8}$a s v
e) $\dfrac{8x+2y}{20x+5y}$a s v
f) $\dfrac{4x^2+20x}{6x+30}$a s v
g) $\dfrac{6y^3-15y^2}{24y^2-60y}$a s v
h) $\dfrac{24a^4-40a^3}{60a^6-100a^5}$a s v

## Question 12

Simplify using any method

a) $\dfrac{4x^2+6x+2}{10}$a s v
b) $\dfrac{18p^4-15p}{33+15p^3}$a s v
c) $\dfrac{15x^3+15x^2y}{5x^2+5xy}$a s v
d) $\dfrac{x-2}{2-x}$a s v
e) $\dfrac{5(x-9)}{9-x}$a s v
f) $\dfrac{7x-35}{5-x}$a s v
g) $\dfrac{3x^2-33x}{44-4x}$a s v
h) $\dfrac{40y^2-100y}{20y^2-8y^3}$a s v

## Question 13

Factorise and simplify

a) $\dfrac{x^2+2x}{x^2+3x+2}$a s v
b) $\dfrac{x^2+7x+10}{2x^2+10x}$a s v
c) $\dfrac{x^2+4x+3}{x^2+9x+18}$a s v
d) $\dfrac{x^2+14x+45}{x^2+9x+20}$a s v
e) $\dfrac{x^2+13x+30}{x+10}$a s v
f) $\dfrac{x^2+3x-18}{x^2+8x+12}$a s v
g) $\dfrac{x^2-6x+8}{x^2-9x+14}$a s v
h) $\dfrac{x^2-14x+49}{x^2-16x+63}$a s v

## Question 14

Factorise and simplify

a) $\dfrac{3x^2+9x}{2x^2+7x+3}$a s v
b) $\dfrac{2x^2+19x+35}{10x^2+25x}$a s v
c) $\dfrac{3x^2+7x+2}{3x^2+10x+3}$a s v
d) $\dfrac{5x^2+32x+12}{5x^2-8x-4}$a s v
e) $\dfrac{9x^2+16x+5}{6x^2+19x+15}$a s v
f) $\dfrac{4x^2+28x+49}{10x^2+37x+7}$a s v
g) $\dfrac{12x^2+29x-8}{9x^2+21x-8}$a s v
h) $\dfrac{6x^2-43x+72}{8x^2-54x+81}$a s v

## Question 15

Factorise and simplify

a) $\dfrac{3x^2+24x+45}{x^3+11x^2+30x}$a s v
b) $\dfrac{4x^3+60x^2+224x}{9x^2+54x-144}$a s v
c) $\dfrac{y^4-10y^3+16y^2}{60y-4y^2-216}$a s v
d) $\dfrac{42a^2-315a+525}{315a-36a^2-36a^3}$a s v
The content structure consists of a series of algebraic simplification questions, each with multiple parts (a) through (f) or (h), and placeholders for answers (a), solutions (s), and videos (v).
multiple_questions
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Algebra - Simplifying Algebraic Fractions

a - answer    s - solution    v - video

## Question 1

Simplify

a) $\dfrac{6x}{4}$a s v
b) $\dfrac{8x}{6}$a s v
c) $\dfrac{8x}{10}$a s v
d) $\dfrac{21x^2}{14}$a s v
e) $\dfrac{46y}{2}$a s v
f) $\dfrac{9\sqrt{a}}{27}$a s v

## Question 2

Simplify

a) $\dfrac{15}{10x}$a s v
b) $\dfrac{40}{30y}$a s v
c) $\dfrac{16}{4p}$a s v
d) $\dfrac{48}{20a^3}$a s v
e) $\dfrac{9}{14h}$a s v
f) $\dfrac{36}{32m}$a s v

## Question 3

Simplify

a) $\dfrac{2y}{3y}$a s v
b) $\dfrac{10x}{4x}$a s v
c) $\dfrac{15z}{5z}$a s v
d) $\dfrac{5x^2}{5x^2}$a s v
e) $\dfrac{2\sqrt{y}}{7\sqrt{y}}$a s v
f) $\dfrac{48y^5}{36y^5}$a s v

## Question 4

Simplify

a) $\dfrac{3x^2}{2x}$a s v
b) $\dfrac{9p^3}{5p}$a s v
c) $\dfrac{5y^2}{y}$a s v
d) $\dfrac{16z^5}{12z^2}$a s v
e) $\dfrac{21q^8}{35q^3}$a s v
f) $\dfrac{44c^{12}}{20c^{12}}$a s v

## Question 5

Simplify

a) $\dfrac{4x}{5x^3}$a s v
b) $\dfrac{8x^2}{6x^5}$a s v
c) $\dfrac{9v^3}{15v^3}$a s v
d) $\dfrac{35y^4}{50y^{17}}$a s v
e) $\dfrac{42a^4}{24a^5}$a s v
f) $\dfrac{19t^{13}}{3t^{13}}$a s v

## Question 6

Simplify

a) $\dfrac{2(x+1)}{3(x+1)}$a s v
b) $\dfrac{18(y-2)}{6(y-2)}$a s v
c) $\dfrac{22(x^2+4)}{10(x+1)}$a s v
d) $\dfrac{15(x-1)}{39(x-1)^2}$a s v
e) $\dfrac{77(2x+3)^3}{44(2x+3)}$a s v
f) $\dfrac{8(4z^2+5)^8}{11(4z^2+5)^{10}}$a s v

## Question 7

Simplify

a) $\dfrac{x^2y}{x}$a s v
b) $\dfrac{4xy^7}{xy^2}$a s v
c) $\dfrac{20x^4y^2}{15x^3}$a s v
d) $\dfrac{10a^6}{25a^2b^5}$a s v
e) $\dfrac{4x(x+5)}{3(x+5)}$a s v
f) $\dfrac{48h^2(g-3)}{40h}$a s v

## Question 8

Simplify. Leave answers with positive indices

a) $\dfrac{5x}{x^{-2}y}$a s v
b) $\dfrac{4y^{-3}}{xy}$a s v
c) $\dfrac{2x^{-5}y^{-3}}{10x^{-1}y^{-2}}$a s v
d) $\dfrac{15a^{-2}b^{-5}}{6a^{-6}bc^{-1}}$a s v
e) $\dfrac{21x^{-3}y^4z}{56x^{-8}y^{-1}z^3}$a s v
f) $\dfrac{108m^{-9}npq^{-15}}{60m^{-2}n^{-12}p^5}$a s v

## Question 9

Simplify. Leave answers with positive indices

a) $\dfrac{-4a^2bc}{2ab^2}$a s v
b) $\dfrac{10xy^3}{-6xyz}$a s v
c) $\dfrac{-8p^3q^2r}{-20pq^2r^3}$a s v
d) $\dfrac{45p^{-2}q^4}{25p^7q^{-1}}$a s v
e) $\dfrac{33c^{-1}d^{-7}e}{-21c^{-1}d^3e^8}$a s v
f) $\dfrac{-27w^{-3}x^{14}y^{-9}z}{-63w^2x^{-3}z^{15}}$a s v

## Question 10

Factorise and simplify

a) $\dfrac{6x+4}{4}$a s v
b) $\dfrac{8p-14}{2}$a s v
c) $\dfrac{15w+35}{20}$a s v
d) $\dfrac{21a-30}{12}$a s v
e) $\dfrac{18a^2-20a}{14a}$a s v
f) $\dfrac{42g^2-66g^5}{24g^3}$a s v

## Question 11

Factorise and simplify

a) $\dfrac{4x+8}{6x+12}$a s v
b) $\dfrac{9x+3}{3x+1}$a s v
c) $\dfrac{x^2+3x}{2x+6}$a s v
d) $\dfrac{xy-2y}{4x-8}$a s v
e) $\dfrac{8x+2y}{20x+5y}$a s v
f) $\dfrac{4x^2+20x}{6x+30}$a s v
g) $\dfrac{6y^3-15y^2}{24y^2-60y}$a s v
h) $\dfrac{24a^4-40a^3}{60a^6-100a^5}$a s v

## Question 12

Simplify using any method

a) $\dfrac{4x^2+6x+2}{10}$a s v
b) $\dfrac{18p^4-15p}{33+15p^3}$a s v
c) $\dfrac{15x^3+15x^2y}{5x^2+5xy}$a s v
d) $\dfrac{x-2}{2-x}$a s v
e) $\dfrac{5(x-9)}{9-x}$a s v
f) $\dfrac{7x-35}{5-x}$a s v
g) $\dfrac{3x^2-33x}{44-4x}$a s v
h) $\dfrac{40y^2-100y}{20y^2-8y^3}$a s v

## Question 13

Factorise and simplify

a) $\dfrac{x^2+2x}{x^2+3x+2}$a s v
b) $\dfrac{x^2+7x+10}{2x^2+10x}$a s v
c) $\dfrac{x^2+4x+3}{x^2+9x+18}$a s v
d) $\dfrac{x^2+14x+45}{x^2+9x+20}$a s v
e) $\dfrac{x^2+13x+30}{x+10}$a s v
f) $\dfrac{x^2+3x-18}{x^2+8x+12}$a s v
g) $\dfrac{x^2-6x+8}{x^2-9x+14}$a s v
h) $\dfrac{x^2-14x+49}{x^2-16x+63}$a s v

## Question 14

Factorise and simplify

a) $\dfrac{3x^2+9x}{2x^2+7x+3}$a s v
b) $\dfrac{2x^2+19x+35}{10x^2+25x}$a s v
c) $\dfrac{3x^2+7x+2}{3x^2+10x+3}$a s v
d) $\dfrac{5x^2+32x+12}{5x^2-8x-4}$a s v
e) $\dfrac{9x^2+16x+5}{6x^2+19x+15}$a s v
f) $\dfrac{4x^2+28x+49}{10x^2+37x+7}$a s v
g) $\dfrac{12x^2+29x-8}{9x^2+21x-8}$a s v
h) $\dfrac{6x^2-43x+72}{8x^2-54x+81}$a s v

## Question 15

Factorise and simplify

a) $\dfrac{3x^2+24x+45}{x^3+11x^2+30x}$a s v
b) $\dfrac{4x^3+60x^2+224x}{9x^2+54x-144}$a s v
c) $\dfrac{y^4-10y^3+16y^2}{60y-4y^2-216}$a s v
d) $\dfrac{42a^2-315a+525}{315a-36a^2-36a^3}$a s v
user
The content structure consists of a series of algebraic simplification questions, each with multiple parts (a) through (f) or (h), and placeholders for answers (a), solutions (s), and videos (v).

TYPE: MULTIPLE_QUESTIONS