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

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

Solve for n

$$n=9$$

Steps for Solving Linear Equation

Variable n cannot be equal to any of the values -1,5 since division by zero is not defined. Multiply both sides of the equation by \left(n-5\right)\left(n+1\right), the least common multiple of n-5,n+1.

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

Use the distributive property to multiply n+1 by 2.

$$2n+2=\left(n-5\right)\times 5$$

Use the distributive property to multiply n-5 by 5.

$$2n+2=5n-25$$

Subtract 5n from both sides.

$$2n+2-5n=-25$$

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

$$-3n+2=-25$$

Subtract 2 from both sides.

$$-3n=-25-2$$

Subtract 2 from -25 to get -27.

$$-3n=-27$$

Divide both sides by -3.

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

Divide -27 by -3 to get 9.

$$n=9$$