# Solve for m (if(3m+2y))/(5m-4y)=9/4

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.
Simplify by multiplying through.
Apply the distributive property.
Reorder.
Rewrite using the commutative property of multiplication.
Rewrite using the commutative property of multiplication.
Simplify each term.
Move to the left of .
Move to the left of .
Simplify by multiplying through.
Apply the distributive property.
Multiply.
Multiply by .
Multiply by .
Multiply the expression by a factor of to create the least common denominator (LCD) of .
Simplify.
Apply the distributive property.
Multiply.
Multiply by .
Multiply by .
Since the expression on each side of the equation has the same denominator, the numerators must be equal.
Subtract from both sides of the equation.
Subtract from 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 .
Simplify .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify .
Simplify each term.
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
Move the negative in front of the fraction.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Multiply and .
Reorder the factors of .
Combine the numerators over the common denominator.
Simplify the numerator.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Multiply by .
Simplify with factoring out.
Rewrite as .
Factor out of .
Factor out of .
Simplify the expression.
Move the negative in front of the fraction.
Reorder factors in .
Solve for m (if(3m+2y))/(5m-4y)=9/4

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