What is the answer to (3x-7)/x =(8x)/(x+1)-5 ?

The answer to (3x-7)/x =(8x)/(x+1)-5 is x=7

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(3x-7)/x =(8x)/(x+1)-5

\frac{3 x - 7}{x} = \frac{8 x}{x + 1} - 5

x = 7

Solution steps

\frac{3 x - 7}{x} = \frac{8 x}{x + 1} - 5

Multiply by LCM

(3 x - 7) (x + 1) = 8 x^{2} - 5 x (x + 1)

Expand

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

3 x^{2} - 4 x - 7 = 8 x^{2} - 5 x^{2} - 5 x

Add similar elements:

8 x^{2} - 5 x^{2} = 3 x^{2}

3 x^{2} - 4 x - 7 = 3 x^{2} - 5 x

Expand

(3 x - 7) (x + 1) : 3 x^{2} - 4 x - 7

3 x^{2} - 4 x - 7 = 3 x^{2} - 5 x

Move

7

to the right side

3 x^{2} - 4 x = 3 x^{2} - 5 x + 7

Subtract

3 x^{2} - 5 x

from both sides

3 x^{2} - 4 x - (3 x^{2} - 5 x) = 3 x^{2} - 5 x + 7 - (3 x^{2} - 5 x)

Simplify

x = 7

Verify Solutions

Find undefined (singularity) points:

x = 0, x = - 1

Combine undefined points with solutions:

x = 7

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

\frac{6}{x} - 3 = \frac{7}{5}

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

\frac{5 x}{x - 5} - 1 = \frac{1}{x - 5}

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

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