What is the answer to ((2x^2+x-5))/((x-5))=((x^2+x-6))/((x-6)) ?

The answer to ((2x^2+x-5))/((x-5))=((x^2+x-6))/((x-6)) is x=0,x=7

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((2x^2+x-5))/((x-5))=((x^2+x-6))/((x-6))

\frac{( 2 x ^{2} + x - 5 )}{( x - 5 )} = \frac{( x ^{2} + x - 6 )}{( x - 6 )}

x = 0, x = 7

Solution steps

\frac{( 2 x ^{2} + x - 5 )}{( x - 5 )} = \frac{( x ^{2} + x - 6 )}{( x - 6 )}

Cross multiply

(2 x^{2} + x - 5) (x - 6) = (x - 5) (x^{2} + x - 6)

Solve

(2 x^{2} + x - 5) (x - 6) = (x - 5) (x^{2} + x - 6) : x = 0, x = 7

x = 0, x = 7

Verify Solutions

Find undefined (singularity) points:

x = 5, x = 6

Combine undefined points with solutions:

x = 0, x = 7

\frac{15}{4 - 7 x} = 9

- x^{- 1} = 4

\frac{x ^{2} + 1}{x ^{2}} = 3

\frac{17}{8 y} = \frac{41}{2}

x, \frac{6}{x} + \frac{12}{y} = 2

What is the answer to ((2x^2+x-5))/((x-5))=((x^2+x-6))/((x-6)) ?
The answer to ((2x^2+x-5))/((x-5))=((x^2+x-6))/((x-6)) is x=0,x=7
Solve for x: ((2x^2+x-5))/((x-5))=((x^2+x-6))/((x-6))
The solution is x=0,x=7