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

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

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

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

x = 1, x = - 2

Solution steps

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

Multiply by LCM

(x + 2) (x - 5) + (x + 3) (x - 5) = - 7 (x + 3)

Solve

(x + 2) (x - 5) + (x + 3) (x - 5) = - 7 (x + 3) : x = 1, x = - 2

x = 1, x = - 2

Verify Solutions

Find undefined (singularity) points:

x = - 3, x = 5

Combine undefined points with solutions:

x = 1, x = - 2

\frac{4}{x + 2} = \frac{5}{2 x + 1}

\frac{4}{x + 7} = \frac{6}{x}

2 x - \frac{1}{x} = 1

\frac{7}{x - 3} = 2

\frac{1}{3 x - 4} + \frac{1}{5 x + 9} = 6

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