Algebraic fraction expression simplification

Algebraic fractions

 Remember about identifying and removing a common factor first to simplify
the algebraic expression.
 Common factors may be “cancelled out”
 Add “like” terms together.
 If necessary, factorize the remainder expression to obtain solutions for x.




Some exercises for you to do:

20𝑑2 − 50𝑑3 + 10𝑑 𝑥2 + 𝑦2
𝑎) ℎ)
−10𝑑 (𝑥 + 𝑦)2



1 2 1
3𝑏 2 15 𝑥 + 𝑥2 + 𝑥3
𝑏) ÷ 𝑖)
8𝑎 4 (𝑥 + 1)2



𝑥 𝑎 𝑐 3 4−𝑝 3
𝑐) ÷( × ) 𝑗) − +
𝑦 𝑏 𝑑 2 8𝑝 4𝑝



3 2 3−𝑥 3−𝑥 3−𝑥
𝑑) + 𝑘) + −
𝑥 𝑦 3𝑥 3 3𝑥 2



3 2 4𝑡 2 𝑘 4 − 𝑘 3 2𝑡
𝑒) 2 + 2 𝑙) × ÷
𝑥 𝑦 3𝑘 3 2𝑡 3



1 1
𝑎 + 3𝑥 2 − 8𝑥
𝑓) 𝑏 𝑚)
1 3𝑥 2
𝑎+𝑏



60𝑥 6 𝑦 3 − 15𝑥 4 𝑦 4
𝑔)
−5𝑥 3 𝑦 2

, Memorandum


20𝑑2 − 50𝑑3 + 10𝑑
𝑎)
−10𝑑
10𝑑(2𝑑 − 5𝑑2 + 1)
= (𝑐𝑜𝑚𝑚𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟 𝑜𝑓 10𝑑)
−10𝑑

= −(2𝑑 − 5𝑑2 + 1)

= −2𝑑 + 5𝑑2 − 1



3𝑏 2 15
𝑏) ÷
8𝑎 4
3𝑏 2 4
= ×
8𝑎 15

1𝑏 2 1
= ×
2𝑎 5

𝑏2
=
10𝑎



𝑥 𝑎 𝑐
𝑐) ÷( × )
𝑦 𝑏 𝑑
𝑥 𝑎𝑐
= ÷( )
𝑦 𝑏𝑑

𝑥 𝑏𝑑
= ×( )
𝑦 𝑎𝑐

𝑥𝑏𝑑
=
𝑦𝑎𝑐

3 2
𝑑) +
𝑥 𝑦

3𝑦 + 2𝑥
=
𝑥𝑦