What is the answer to (2x-5)/(x+10)= 1/(x-6) ?

The answer to (2x-5)/(x+10)= 1/(x-6) is x=(9+sqrt(41))/2 ,x=(9-sqrt(41))/2

Solve for x: (2x-5)/(x+10)= 1/(x-6)

The solution is x=(9+sqrt(41))/2 ,x=(9-sqrt(41))/2

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\frac{2 x - 5}{x + 10} = \frac{1}{x - 6}

x = \frac{9 + 41}{2}, x = \frac{9 - 41}{2}

Decimal Notation

x = 7.70156 \dots, x = 1.29843 \dots

Solution steps

\frac{2 x - 5}{x + 10} = \frac{1}{x - 6}

Cross multiply

(2 x - 5) (x - 6) = x + 10

Solve

(2 x - 5) (x - 6) = x + 10 : x = \frac{9 + 41}{2}, x = \frac{9 - 41}{2}

x = \frac{9 + 41}{2}, x = \frac{9 - 41}{2}

Verify Solutions

Find undefined (singularity) points:

x = - 10, x = 6

Combine undefined points with solutions:

x = \frac{9 + 41}{2}, x = \frac{9 - 41}{2}

\frac{3 x - 6}{7 x + 7} = 0

\frac{5}{4 x} = - \frac{11}{6}

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

\frac{8}{2 \cdot ( a + 2 )} = 1

\frac{3 m + 1}{3 m - 1} - \frac{3 m - 1}{3 m + 1} = 2

What is the answer to (2x-5)/(x+10)= 1/(x-6) ?
The answer to (2x-5)/(x+10)= 1/(x-6) is x=(9+sqrt(41))/2 ,x=(9-sqrt(41))/2
Solve for x: (2x-5)/(x+10)= 1/(x-6)
The solution is x=(9+sqrt(41))/2 ,x=(9-sqrt(41))/2