What is the answer to (8x-5)/(2x+5)=5-(3x+7)/(3x+2) ?

The answer to (8x-5)/(2x+5)=5-(3x+7)/(3x+2) is x=-5/13

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(8x-5)/(2x+5)=5-(3x+7)/(3x+2)

\frac{8 x - 5}{2 x + 5} = 5 - \frac{3 x + 7}{3 x + 2}

x = - \frac{5}{13}

Decimal Notation

x = - 0.38461 \dots

Solution steps

\frac{8 x - 5}{2 x + 5} = 5 - \frac{3 x + 7}{3 x + 2}

Multiply by LCM

24 x^{2} + x - 10 = 24 x^{2} + 66 x + 15

Move

10

to the right side

24 x^{2} + x = 24 x^{2} + 66 x + 25

Subtract

24 x^{2} + 66 x

from both sides

24 x^{2} + x - (24 x^{2} + 66 x) = 24 x^{2} + 66 x + 25 - (24 x^{2} + 66 x)

Simplify

- 65 x = 25

Divide both sides by

- 65

x = - \frac{5}{13}

Verify Solutions

Find undefined (singularity) points:

x = - \frac{5}{2}, x = - \frac{2}{3}

Combine undefined points with solutions:

x = - \frac{5}{13}

\frac{1}{x + 6} + \frac{12}{x ^{2} - 36} = 1

\frac{y}{4} = \frac{9}{y}

\frac{b}{a x - 1} - \frac{a}{b x - 1} = 0

6 (1 - x^{2})^{- 1} + 3 (1 - x)^{- 1} = 5 (x + 1)^{- 1}

\frac{3}{5} + \frac{7}{6 x} = \frac{1}{8 x}

What is the answer to (8x-5)/(2x+5)=5-(3x+7)/(3x+2) ?
The answer to (8x-5)/(2x+5)=5-(3x+7)/(3x+2) is x=-5/13
Solve for x: (8x-5)/(2x+5)=5-(3x+7)/(3x+2)
The solution is x=-5/13