What is the answer to ((x(x-1)))/((x^2+x-2))= x/((x+5)) ?

The answer to ((x(x-1)))/((x^2+x-2))= x/((x+5)) is x=0

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((x(x-1)))/((x^2+x-2))= x/((x+5))

\frac{( x ( x - 1 ) )}{( x ^{2} + x - 2 )} = \frac{x}{( x + 5 )}

x = 0

Solution steps

\frac{( x ( x - 1 ) )}{( x ^{2} + x - 2 )} = \frac{x}{( x + 5 )}

Cross multiply

x^{2} + 5 x = x^{2} + 2 x

Subtract

x^{2} + 2 x

from both sides

x^{2} + 5 x - (x^{2} + 2 x) = x^{2} + 2 x - (x^{2} + 2 x)

Simplify

3 x = 0

Divide both sides by

3

x = 0

Verify Solutions

Find undefined (singularity) points:

x = - 2, x = 1, x = - 5

Combine undefined points with solutions:

x = 0

a^{5} + \frac{1}{a ^{5}} = 123, a + \frac{1}{a}

\frac{2}{( 3 x - 1 )} + \frac{3}{( 3 x + 1 )} = \frac{5}{3} x

x + \frac{4}{x} - 4 + x - \frac{4}{x} + 4 = \frac{10}{3}

\frac{x}{( 1 - x )} + \frac{( 1 - x )}{x} = \frac{21}{6}

\frac{24}{3 a} = 4

What is the answer to ((x(x-1)))/((x^2+x-2))= x/((x+5)) ?
The answer to ((x(x-1)))/((x^2+x-2))= x/((x+5)) is x=0
Solve for x: ((x(x-1)))/((x^2+x-2))= x/((x+5))
The solution is x=0