Solve 5/3n-15-1/3=-5/n-5

$$\frac { 5 } { 3 n - 15 } - \frac { 1 } { 3 } = \frac { - 5 } { n - 5 }$$

Solve for n

$$n=25$$

Steps for Solving Linear Equation

Variable n cannot be equal to 5 since division by zero is not defined. Multiply both sides of the equation by 3\left(n-5\right), the least common multiple of 3n-15,3,n-5.

$$5+3\left(n-5\right)\left(-\frac{1}{3}\right)=3\left(-5\right)$$

Multiply 3 and -\frac{1}{3} to get -1.

$$5-\left(n-5\right)=3\left(-5\right)$$

To find the opposite of n-5, find the opposite of each term.

$$5-n+5=3\left(-5\right)$$

Add 5 and 5 to get 10.

$$10-n=3\left(-5\right)$$

Multiply 3 and -5 to get -15.

$$10-n=-15$$

Subtract 10 from both sides.

$$-n=-15-10$$

Subtract 10 from -15 to get -25.

$$-n=-25$$

Multiply both sides by -1.

$$n=25$$