Question

Simplify into one fraction

7/x-3 + 3/x-5

simplify into one fraction
-5/x-3 - -4.x+2

simplify into one fraction
6/x+7 - 3/x-2

Answer 1

1. 10x-44/x(squared)-8x+15
2. X+22/x(squared) -x-6
3.3x-33/x(squared)+5x-14

Answer 2

Answer and Explanation :

We have simplify the expressions into one fraction :

1) Expression
`(7)/(x-3)+ (3)/(x-5)`

Taking LCM in the denominator,

`=(7(x-5)+3(x-3))/((x-3)(x-5))`

`=(7x-35+3x-9)/(x^2-5x-3x+15)`

`=(10x-44)/(x^2-8x+15)`

The required form is
`(7)/(x-3)+ (3)/(x-5)=(10x-44)/(x^2-8x+15)`

2) Expression
`(-5)/(x-3)-(-4\cdot(x+2))`

Taking LCM in the denominator,

`(-5)/(x-3)+(4x+8)`

`=(-5+(4x+8)(x-3)))/(x-3)`

`=(-5+4x^2-12x+8x-24)/(x-3)`

`=(4x^2-4x-29)/(x-3)`

The required form is
`(-5)/(x-3)-(-4\cdot(x+2))=(4x^2-4x-29)/(x-3)`

3) Expression
`(6)/(x+7)- (3)/(x-2)`

Taking LCM in the denominator,

`=(6(x-2)-3(x+7))/((x+7)(x-2))`

`=(6x-12-3x-21)/(x^2-2x+7x-14)`

`=(3x-33)/(x^2+6x-14)`

The required form is
`(6)/(x+7)- (3)/(x-2)=(3x-33)/(x^2+6x-14)`