What is the answer to (9x+10)/(3x-8)=(12x-8)/(4x-5) ?

The answer to (9x+10)/(3x-8)=(12x-8)/(4x-5) is x= 114/115

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(9x+10)/(3x-8)=(12x-8)/(4x-5)

\frac{9 x + 10}{3 x - 8} = \frac{12 x - 8}{4 x - 5}

x = \frac{114}{115}

Decimal Notation

x = 0.99130 \dots

Solution steps

\frac{9 x + 10}{3 x - 8} = \frac{12 x - 8}{4 x - 5}

Cross multiply

36 x^{2} - 5 x - 50 = 36 x^{2} - 120 x + 64

Move

50

to the right side

36 x^{2} - 5 x = 36 x^{2} - 120 x + 114

Subtract

36 x^{2} - 120 x

from both sides

36 x^{2} - 5 x - (36 x^{2} - 120 x) = 36 x^{2} - 120 x + 114 - (36 x^{2} - 120 x)

Simplify

115 x = 114

Divide both sides by

115

x = \frac{114}{115}

Verify Solutions

Find undefined (singularity) points:

x = \frac{8}{3}, x = \frac{5}{4}

Combine undefined points with solutions:

x = \frac{114}{115}

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

1 + \frac{2}{x - 3} = \frac{5}{x ^{2} - 9}

2 x^{- 3} = 54

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

\frac{x ^{2}}{x - 1} = \frac{x ^{2} - 16}{x + 4}

What is the answer to (9x+10)/(3x-8)=(12x-8)/(4x-5) ?
The answer to (9x+10)/(3x-8)=(12x-8)/(4x-5) is x= 114/115
Solve for x: (9x+10)/(3x-8)=(12x-8)/(4x-5)
The solution is x= 114/115