Solve 3/x-1+3/10=5/2x-2

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

Solve for x

$$x=-\frac{2}{3}\approx -0.666666667$$

Steps for Solving Linear Equation

Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by 10\left(x-1\right), the least common multiple of x-1,10,2x-2.

$$10\times 3+10\left(x-1\right)\times \frac{3}{10}=5\times 5$$

Multiply 10 and 3 to get 30.

$$30+10\left(x-1\right)\times \frac{3}{10}=5\times 5$$

Multiply 10 and \frac{3}{10} to get 3.

$$30+3\left(x-1\right)=5\times 5$$

Use the distributive property to multiply 3 by x-1.

$$30+3x-3=5\times 5$$

Subtract 3 from 30 to get 27.

$$27+3x=5\times 5$$

Multiply 5 and 5 to get 25.

$$27+3x=25$$

Subtract 27 from both sides.

$$3x=25-27$$

Subtract 27 from 25 to get -2.

$$3x=-2$$

Divide both sides by 3.

$$x=\frac{-2}{3}$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$x=-\frac{2}{3}$$