help simplify

Question

c)    x over  x²-3x-4    –     4 over x+1  

help me simplify and how to check the answer if correct.

Answer 1

The expression is [x/(x² - 3x - 4)] - [4/(x + 1)]

= [x/(x + 1)(x - 4)] - [4/(x + 1)]

= [x - 4(x - 4)]/[(x + 1)(x - 4)]

= (x - 4x + 16)/[(x + 1)(x - 4)]

= (- 3x + 16)/[(x + 1)(x - 4)]

[x/(x² - 3x - 4)] - [4/(x + 1)] = (- 3x + 16)/[(x + 1)(x - 4)].

Check :

[x/(x² - 3x - 4)] - [4/(x + 1)] = (- 3x + 16)/[(x + 1)(x - 4)]

Let x = 1

Substitute  x = 1 in left hand side expression.

[x/(x² - 3x - 4)] - [4/(x + 1)]

= [1/(1² - 3(1) - 4)] - [4/(1 + 1)]

= 1/(1 - 3 - 4) - (4/2)

= (- 1/6)- 2

= (- 1 - 12)/6

= - 13/6

Substitute  x = 1 in right hand side expression.

(- 3x + 16)/[(x + 1)(x - 4)]

= [- 3(1) + 16]/[(1 + 1)(1 - 4)]

= [- 3 + 16]/[2( - 3)]

= - 13/6

 At x = 1, both expressions value is - 13/6.

Therefore, [x/(x² - 3x - 4)] - [4/(x + 1)] = (- 3x + 16)/[(x + 1)(x - 4)].