What is the answer to 1+1/(x-5)= 3/(x^2-7x+10) ?

The answer to 1+1/(x-5)= 3/(x^2-7x+10) is x=1

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1+1/(x-5)= 3/(x^2-7x+10)

1 + \frac{1}{x - 5} = \frac{3}{x ^{2} - 7 x + 10}

x = 1

Solution steps

1 + \frac{1}{x - 5} = \frac{3}{x ^{2} - 7 x + 10}

Multiply by LCM

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

Solve

(x - 5) (x - 2) + x - 2 = 3 : x = 5, x = 1

x = 5, x = 1

Verify Solutions

Find undefined (singularity) points:

x = 5, x = 2

Since the equation is undefined for:

5

x = 1

x + \frac{1}{x} = 35

\frac{x - 1}{x + 1} + \frac{4}{x + 5} = 1

\frac{10}{x + 8} = \frac{5}{x - 8}

2 x - \frac{27648}{x ^{2}} = 0

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

What is the answer to 1+1/(x-5)= 3/(x^2-7x+10) ?
The answer to 1+1/(x-5)= 3/(x^2-7x+10) is x=1
Solve for x: 1+1/(x-5)= 3/(x^2-7x+10)
The solution is x=1