What is the answer to (x-13)/x =5-(10(5x+3))/(x^2) ?

The answer to (x-13)/x =5-(10(5x+3))/(x^2) is x=10,x=-3/4

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(x-13)/x =5-(10(5x+3))/(x^2)

\frac{x - 13}{x} = 5 - \frac{10 ( 5 x + 3 )}{x ^{2}}

x = 10, x = - \frac{3}{4}

Decimal Notation

x = 10, x = - 0.75

Solution steps

\frac{x - 13}{x} = 5 - \frac{10 ( 5 x + 3 )}{x ^{2}}

Multiply by LCM

x (x - 13) = 5 x^{2} - 10 (5 x + 3)

Solve

x (x - 13) = 5 x^{2} - 10 (5 x + 3) : x = 10, x = - \frac{3}{4}

x = 10, x = - \frac{3}{4}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = 10, x = - \frac{3}{4}

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

\frac{x + 3}{x} = \frac{2 x + 10}{x - 3}

\frac{2 x}{3} - \frac{1}{x} + \frac{5}{6} = 0

x + \frac{3 x + 2}{x + 4} = 2 x

x + \frac{7}{x - 7} = \frac{x}{x - 7}

What is the answer to (x-13)/x =5-(10(5x+3))/(x^2) ?
The answer to (x-13)/x =5-(10(5x+3))/(x^2) is x=10,x=-3/4
Solve for x: (x-13)/x =5-(10(5x+3))/(x^2)
The solution is x=10,x=-3/4