What is the answer to (2x+3)/(x-6)=(5x-1)/(4x+7) ?

The answer to (2x+3)/(x-6)=(5x-1)/(4x+7) is x=(-19+sqrt(341))/2 ,x=-(19+sqrt(341))/2

Solve for x: (2x+3)/(x-6)=(5x-1)/(4x+7)

The solution is x=(-19+sqrt(341))/2 ,x=-(19+sqrt(341))/2

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\frac{2 x + 3}{x - 6} = \frac{5 x - 1}{4 x + 7}

x = \frac{- 19 + 341}{2}, x = - \frac{19 + 341}{2}

Decimal

x = - 0.26690 \dots, x = - 18.73309 \dots

Solution steps

\frac{2 x + 3}{x - 6} = \frac{5 x - 1}{4 x + 7}

Cross multiply

(2 x + 3) (4 x + 7) = (x - 6) (5 x - 1)

Solve

(2 x + 3) (4 x + 7) = (x - 6) (5 x - 1) : x = \frac{- 19 + 341}{2}, x = - \frac{19 + 341}{2}

x = \frac{- 19 + 341}{2}, x = - \frac{19 + 341}{2}

Verify Solutions

Find undefined (singularity) points:

x = 6, x = - \frac{7}{4}

Combine undefined points with solutions:

x = \frac{- 19 + 341}{2}, x = - \frac{19 + 341}{2}

\frac{3 x}{x ^{2} - 1} = \frac{x}{x + 1} - 4

1 - \frac{2}{( x - 1 ) ^{2}} = 0

\frac{18}{x ^{3}} = 0

\frac{x ^{2} - 19 x + 84}{x ^{2} - 16 x + 48} = 0

\frac{14}{15} = \frac{26}{x}

What is the answer to (2x+3)/(x-6)=(5x-1)/(4x+7) ?
The answer to (2x+3)/(x-6)=(5x-1)/(4x+7) is x=(-19+sqrt(341))/2 ,x=-(19+sqrt(341))/2
Solve for x: (2x+3)/(x-6)=(5x-1)/(4x+7)
The solution is x=(-19+sqrt(341))/2 ,x=-(19+sqrt(341))/2