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# Simplifying this rational expression?

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

Aug 8, 2018

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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