What is the answer to 1+7/(x-4)= 5/(x^2+3x-28) ?

The answer to 1+7/(x-4)= 5/(x^2+3x-28) is x=-2,x=-8

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1+7/(x-4)= 5/(x^2+3x-28)

1 + \frac{7}{x - 4} = \frac{5}{x ^{2} + 3 x - 28}

x = - 2, x = - 8

Solution steps

1 + \frac{7}{x - 4} = \frac{5}{x ^{2} + 3 x - 28}

Multiply by LCM

(x - 4) (x + 7) + 7 (x + 7) = 5

Solve

(x - 4) (x + 7) + 7 (x + 7) = 5 : x = - 2, x = - 8

x = - 2, x = - 8

Verify Solutions

Find undefined (singularity) points:

x = 4, x = - 7

Combine undefined points with solutions:

x = - 2, x = - 8

\frac{18}{x} = x - 3

26 - \frac{1}{x ^{2}} = 0

\frac{7 x - 3}{5 x + 12} = \frac{4 x - 1}{3 x + 4}

\frac{- 9}{\frac{1}{8}} = \frac{36}{x}

\frac{8}{x - 1} = \frac{4}{3}

What is the answer to 1+7/(x-4)= 5/(x^2+3x-28) ?
The answer to 1+7/(x-4)= 5/(x^2+3x-28) is x=-2,x=-8
Solve for x: 1+7/(x-4)= 5/(x^2+3x-28)
The solution is x=-2,x=-8