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

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

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(5+x)/(3x-4)= 4/(x+1)+1

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

x = - 5, x = \frac{5}{2}

Decimal Notation

x = - 5, x = 2.5

Solution steps

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

Multiply by LCM

(5 + x) (x + 1) = 4 (3 x - 4) + (x + 1) (3 x - 4)

Solve

(5 + x) (x + 1) = 4 (3 x - 4) + (x + 1) (3 x - 4) : x = - 5, x = \frac{5}{2}

x = - 5, x = \frac{5}{2}

Verify Solutions

Find undefined (singularity) points:

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

Combine undefined points with solutions:

x = - 5, x = \frac{5}{2}

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

\frac{2 x}{x + 1} + 6 = \frac{2}{x ^{2} + x}

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

5 - \frac{100}{x ^{2}} = 0

\frac{x - 4}{x} = \frac{2 x + 10}{x + 4}

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