Problem

Simplify. \[ \frac{4-y^{2}}{y^{2}-3 y-10} \]

Solution

Step 1 :Factorize the numerator \(4-y^{2}\) as a difference of squares to get \((2-y)(2+y)\).

Step 2 :Factorize the denominator \(y^{2}-3 y-10\) as a quadratic expression to get \((y-5)(y+2)\).

Step 3 :Cancel out the common factors in the numerator and the denominator.

Step 4 :The simplified form of the given expression is \(\boxed{\frac{2-y}{y-5}}\)

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