What is the answer to ((x-5))/x-((x-7))/((x-1))= 5/x ?

The answer to ((x-5))/x-((x-7))/((x-1))= 5/x is x= 5/2

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((x-5))/x-((x-7))/((x-1))= 5/x

\frac{( x - 5 )}{x} - \frac{( x - 7 )}{( x - 1 )} = \frac{5}{x}

x = \frac{5}{2}

Decimal Notation

x = 2.5

Solution steps

\frac{( x - 5 )}{x} - \frac{( x - 7 )}{( x - 1 )} = \frac{5}{x}

Multiply by LCM

x + 5 = 5 x - 5

Move

5

to the right side

x = 5 x - 10

Move

5 x

to the left side

- 4 x = - 10

Divide both sides by

- 4

x = \frac{5}{2}

Verify Solutions

Find undefined (singularity) points:

x = 0, x = 1

Combine undefined points with solutions:

x = \frac{5}{2}

y = \frac{1}{( 4 - y ^{2} )}

b, \frac{1}{d ^{2}} = \frac{1}{b ^{2}} + \frac{1}{c ^{2}}

a, a - c = 2 \frac{( a + b )}{a}

e^{l} n x = \frac{x ^{1}}{x}

(\frac{3}{4 x + 1})^{3} - (x + 2)^{3} + (0.25 x + 1)^{3} = 0

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