How do you simplify $\frac{5}{x + 3} - \frac{2}{x - 1}$ $5/(x+3) - 2/(x-1)$ ?

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How do you simplify $\frac{5}{x + 3} - \frac{2}{x - 1}$ $5/(x+3) - 2/(x-1)$ ?

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Answer 1 · 2018-03-24T04:03:18

$\frac{3 x - 11}{(x + 3) (x - 1)}$ $(3x-11)/((x+3)(x-1))$
Where $x \neq - 3 or 1$ $x!=-3 or 1$

Explanation:

$\frac{3 x - 11}{(x + 3) (x - 1)}$ $(3x-11)/((x+3)(x-1))$
Where $x \neq - 3 or 1$ $x!=-3 or 1$
The reason x can't be -3 or 1 is because if this happens the denominator will become $0$ $0$ and anything with denominator $0$ $0$ becomes undefined.
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Answer 2 · 2018-03-24T04:22:51

The given question states :
$\frac{5}{x + 3} - \frac{2}{x - 1}$ $5/(x+3)-2/(x-1)$

So, processing further:
$\Rightarrow \frac{5 \times (x - 1) - 2 \times (x + 3)}{(x + 3) \times (x - 1)}$ $rArr(5 xx( x-1)-2 xx( x+3))/((x+3) xx (x-1)$

$\Rightarrow \frac{(5 x - 5) - (2 x + 6)}{(x + 3) (x - 1)}$ $rArr((5x-5 )-(2x+6))/((x+3) ( x-1)$

$\Rightarrow \frac{5 x - 5 - 2 x - 6}{(x + 3) (x - 1)}$ $rArr(5x-5-2x-6)/((x+3)(x-1)$

$\Rightarrow \frac{5 x - 2 x - 5 - 6}{(x + 3) (x - 1)}$ $rArr(5x-2x -5-6)/((x+3)(x-1)$

$\Rightarrow \frac{3 x - 11}{(x + 3) (x - 1)}$ $rArr(3x-11) /((x+3) (x-1))$

$\Rightarrow \frac{3 x - 11}{x^{2} - x + 3 x - 3}$ $rArr(3x-11) /(x^2-x+3x-3)$

$\Rightarrow \frac{3 x - 11}{x^{2} + 2 x - 3}$ $rArr(3x-11) /(x^2+2x-3)$

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