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

The answer to 5/(x^2+x-6)=2+(x-3)/(x-2) is x=(-1+sqrt(79))/3 ,x=-(1+sqrt(79))/3

Solve for x: 5/(x^2+x-6)=2+(x-3)/(x-2)

The solution is x=(-1+sqrt(79))/3 ,x=-(1+sqrt(79))/3

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\frac{5}{x ^{2} + x - 6} = 2 + \frac{x - 3}{x - 2}

x = \frac{- 1 + 79}{3}, x = - \frac{1 + 79}{3}

Decimal Notation

x = 2.62939 \dots, x = - 3.29606 \dots

Solution steps

\frac{5}{x ^{2} + x - 6} = 2 + \frac{x - 3}{x - 2}

Multiply by LCM

5 = 2 (x - 2) (x + 3) + (x - 3) (x + 3)

Solve

5 = 2 (x - 2) (x + 3) + (x - 3) (x + 3) : x = \frac{- 1 + 79}{3}, x = - \frac{1 + 79}{3}

x = \frac{- 1 + 79}{3}, x = - \frac{1 + 79}{3}

Verify Solutions

Find undefined (singularity) points:

x = - 3, x = 2

Combine undefined points with solutions:

x = \frac{- 1 + 79}{3}, x = - \frac{1 + 79}{3}

x + \frac{9 x}{x - 8} = \frac{72}{x - 8}

1 + \frac{2 x}{x + 4} = - \frac{8}{x + 4}

3.5 = \frac{4 + 2 x}{0.5 - x}

\frac{10}{x} = \frac{2}{9}

\frac{5}{x + 9} = - 2

What is the answer to 5/(x^2+x-6)=2+(x-3)/(x-2) ?
The answer to 5/(x^2+x-6)=2+(x-3)/(x-2) is x=(-1+sqrt(79))/3 ,x=-(1+sqrt(79))/3
Solve for x: 5/(x^2+x-6)=2+(x-3)/(x-2)
The solution is x=(-1+sqrt(79))/3 ,x=-(1+sqrt(79))/3