What is x/(x^2+x-2)-2/(x^2-5x+4) ?

The solution to x/(x^2+x-2)-2/(x^2-5x+4) is (x^2-6x-4)/((x-1)(x+2)(x-4))

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simplify x/(x^2+x-2)-2/(x^2-5x+4)

simplify

\frac{x}{x ^{2} + x - 2} - \frac{2}{x ^{2} - 5 x + 4}

\frac{x ^{2} - 6 x - 4}{( x - 1 ) ( x + 2 ) ( x - 4 )}

Solution steps

\frac{x}{x ^{2} + x - 2} - \frac{2}{x ^{2} - 5 x + 4}

Least Common Multiplier of

x^{2} + x - 2, x^{2} - 5 x + 4 : (x - 1) (x + 2) (x - 4)

Adjust Fractions based on the LCM

= \frac{x ( x - 4 )}{( x - 1 ) ( x + 2 ) ( x - 4 )} - \frac{2 ( x + 2 )}{( x - 1 ) ( x + 2 ) ( x - 4 )}

Apply the fraction rule:

\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

= \frac{x ( x - 4 ) - 2 ( x + 2 )}{( x - 1 ) ( x + 2 ) ( x - 4 )}

Simplify

x (x - 4) - 2 (x + 2) : x^{2} - 6 x - 4

= \frac{x ^{2} - 6 x - 4}{( x - 1 ) ( x + 2 ) ( x - 4 )}

\frac{\frac{x}{4} - \frac{1}{x}}{\frac{x}{2} + 1}

\frac{x ^{4} z ^{5}}{x ^{6} z ^{2}}

\frac{1}{7} + \frac{3}{7}

(2 x + 3) (3 x + 3)

(\frac{3}{2}) (\frac{2}{2})

What is x/(x^2+x-2)-2/(x^2-5x+4) ?
The solution to x/(x^2+x-2)-2/(x^2-5x+4) is (x^2-6x-4)/((x-1)(x+2)(x-4))