Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

Simplify .

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify terms.

Combine the opposite terms in .

Reorder the factors in the terms and .

Subtract from .

Add and .

Simplify each term.

Multiply by .

Multiply by .

Simplify .

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify and combine like terms.

Simplify each term.

Multiply by .

Move to the left of .

Multiply by .

Add and .

Since is on the right side of the equation, switch the sides so it is on the left side of the equation.

Move all terms containing to the left side of the equation.

Subtract from both sides of the equation.

Combine the opposite terms in .

Subtract from .

Add and .

Move all terms not containing to the right side of the equation.

Add to both sides of the equation.

Add and .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Move the negative in front of the fraction.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Solve for n (n-5)/(n+8)=(n-3)/(n+5)