2x2−5xy−12y2x2−16y2\displaystyle \frac{2x^2-5xy-12y^2}{x^2-16y^2} Simplify. Answer ...

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Worked solution

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1. Factorise the quadratic numerator.

2x2−5xy−12y2=(2x+3y)(x−4y)2x^2-5xy-12y^2=(2x+3y)(x-4y)

2. Factorise the denominator using difference of two squares.

x2−16y2=x2−(4y)2=(x−4y)(x+4y)x^2-16y^2=x^2-(4y)^2=(x-4y)(x+4y)

3. Cancel the common factor and write the simplified fraction.

2x2−5xy−12y2x2−16y2=(2x+3y)(x−4y)(x−4y)(x+4y)=2x+3yx+4y\frac{2x^2-5xy-12y^2}{x^2-16y^2}=\frac{(2x+3y)(x-4y)}{(x-4y)(x+4y)}=\frac{2x+3y}{x+4y}

Answer

2x+3yx+4y\frac{2x+3y}{x+4y}

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