What is the answer to 3/(x^2-7x+10)+2=(x-4)/(x-5) ?

The answer to 3/(x^2-7x+10)+2=(x-4)/(x-5) is x=3

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3/(x^2-7x+10)+2=(x-4)/(x-5)

\frac{3}{x ^{2} - 7 x + 10} + 2 = \frac{x - 4}{x - 5}

x = 3

Solution steps

\frac{3}{x ^{2} - 7 x + 10} + 2 = \frac{x - 4}{x - 5}

Multiply by LCM

3 + 2 (x - 2) (x - 5) = (x - 4) (x - 2)

Solve

3 + 2 (x - 2) (x - 5) = (x - 4) (x - 2) : x = 5, x = 3

x = 5, x = 3

Verify Solutions

Find undefined (singularity) points:

x = 2, x = 5

Since the equation is undefined for:

5

x = 3

\frac{4}{x - 3} - \frac{5}{x - 2} = 0

\frac{- 3}{4 x + 3} = \frac{N}{4 x ^{2} - 13 x - 12}

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

\frac{x}{x + 3} + 2 = \frac{9}{x ^{2} + 3 x}

\frac{2 x}{x - 2} = - \frac{30}{x ^{2} - 10 x + 16}

What is the answer to 3/(x^2-7x+10)+2=(x-4)/(x-5) ?
The answer to 3/(x^2-7x+10)+2=(x-4)/(x-5) is x=3
Solve for x: 3/(x^2-7x+10)+2=(x-4)/(x-5)
The solution is x=3