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 $\frac{7}{x-3}+ \frac{3}{x-5}$

Taking LCM in the denominator,

$=\frac{7(x-5)+3(x-3)}{(x-3)(x-5)}$

$=\frac{7x-35+3x-9}{x^2-5x-3x+15}$

$=\frac{10x-44}{x^2-8x+15}$

The required form is $\frac{7}{x-3}+ \frac{3}{x-5}=\frac{10x-44}{x^2-8x+15}$

2) Expression $\frac{-5}{x-3}-(-4\cdot(x+2))$

Taking LCM in the denominator,

$\frac{-5}{x-3}+(4x+8)$

$=\frac{-5+(4x+8)(x-3))}{x-3}$

$=\frac{-5+4x^2-12x+8x-24}{x-3}$

$=\frac{4x^2-4x-29}{x-3}$

The required form is $\frac{-5}{x-3}-(-4\cdot(x+2))=\frac{4x^2-4x-29}{x-3}$

3) Expression $\frac{6}{x+7}- \frac{3}{x-2}$

Taking LCM in the denominator,

$=\frac{6(x-2)-3(x+7)}{(x+7)(x-2)}$

$=\frac{6x-12-3x-21}{x^2-2x+7x-14}$

$=\frac{3x-33}{x^2+6x-14}$

The required form is $\frac{6}{x+7}- \frac{3}{x-2}=\frac{3x-33}{x^2+6x-14}$