# Solve for z (a^2+13)/(a-8)=(17a-59)/(z-8) Rewrite the equation as .
Set up the rational expression with the same denominator over the entire equation.
Multiply each term by a factor of that will equate all the denominators. In this case, all terms need a denominator of . The expression needs to be multiplied by to make the denominator . The expression needs to be multiplied by to make the denominator .
Multiply the expression by a factor of to create the least common denominator (LCD) of .
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 by adding the exponents.
Move .
Multiply by .
Multiply by .
Multiply by .
Subtract from .
Multiply the expression by a factor of to create the least common denominator (LCD) of .
Simplify.
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify each term.
Move to the left of .
Multiply by .
Since the expression on each side of the equation has the same denominator, the numerators must be equal.
Rewrite the equation as .
Move all terms not containing to the right side of the equation.
Add to both sides of the equation.
Add to both sides of the equation.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Combine the numerators over the common denominator.
Solve for z (a^2+13)/(a-8)=(17a-59)/(z-8)

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