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How would i simplify and solve for the non permissible values of this rational expression?

 

 Aug 8, 2018
 #1
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\(\frac{q+2x}{q-4x}\div\frac{q^2-4x^2}{q^2-16x^2}\) Original, unsimplified equation.
\(\frac{q+2x}{q-4x}\cdot\frac{q^2-16x^2}{q^2-4x^2}\) Dividing by a fraction is equal to multiplying by its reciprical.
\(\frac{q+2x}{q-4x}\cdot\frac{(q+4x)(q-4x)}{(q+2x)(q-2x)}\) Applying difference of squares: \(a^2-b^2=(a+b)(a-b)\).
\(\frac{(q+4x)}{(q-2x)}\) Cancelling out like terms. 
\((q+4x)\div(q-2x)\) Final simplified expression

 

I hope this helped,

 

Gavin

 Aug 9, 2018

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