What is the answer to (3x+10}{5x-1}+2=\frac{x-3)/x ?

The answer to (3x+10}{5x-1}+2=\frac{x-3)/x is x=-(6+sqrt(42))/4 ,x=(sqrt(42)-6)/4

Solve for x: (3x+10}{5x-1}+2=\frac{x-3)/x

The solution is x=-(6+sqrt(42))/4 ,x=(sqrt(42)-6)/4

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

x = - \frac{6 + 42}{4}, x = \frac{42 - 6}{4}

Decimal

x = - 3.12018 \dots, x = 0.12018 \dots

Solution steps

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

Multiply by LCM

x (3 x + 10) + 2 x (5 x - 1) = (x - 3) (5 x - 1)

Solve

x (3 x + 10) + 2 x (5 x - 1) = (x - 3) (5 x - 1) : x = - \frac{6 + 42}{4}, x = \frac{42 - 6}{4}

x = - \frac{6 + 42}{4}, x = \frac{42 - 6}{4}

Verify Solutions

Find undefined (singularity) points:

x = \frac{1}{5}, x = 0

Combine undefined points with solutions:

x = - \frac{6 + 42}{4}, x = \frac{42 - 6}{4}

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

- \frac{1}{( x - 2 ) ^{2}} = 0

\frac{5}{x ^{2}} - \frac{43}{x} = 18

- \frac{4 x}{x + 3} + 8 x = 7

\frac{3}{x - 9} + 1 = \frac{4 x}{x - 9}

What is the answer to (3x+10}{5x-1}+2=\frac{x-3)/x ?
The answer to (3x+10}{5x-1}+2=\frac{x-3)/x is x=-(6+sqrt(42))/4 ,x=(sqrt(42)-6)/4
Solve for x: (3x+10}{5x-1}+2=\frac{x-3)/x
The solution is x=-(6+sqrt(42))/4 ,x=(sqrt(42)-6)/4