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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