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

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

Solve for x

$$x=-9$$

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 5\left(x-1\right), the least common multiple of x-1,5.

$$5\left(x+5\right)=2\left(x-1\right)$$

Use the distributive property to multiply 5 by x+5.

$$5x+25=2\left(x-1\right)$$

Use the distributive property to multiply 2 by x-1.

$$5x+25=2x-2$$

Subtract 2x from both sides.

$$5x+25-2x=-2$$

Combine 5x and -2x to get 3x.

$$3x+25=-2$$

Subtract 25 from both sides.

$$3x=-2-25$$

Subtract 25 from -2 to get -27.

$$3x=-27$$

Divide both sides by 3.

$$x=\frac{-27}{3}$$

Divide -27 by 3 to get -9.

$$x=-9$$