Identify Conjugate: Select the conjugate of −5+2.The conjugate of a number of the form a+b is a−b. Therefore, the conjugate of −5+2 is −5−2.
Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator.To rationalize the denominator, we multiply the numerator and the denominator by the conjugate of the denominator.(4⋅(−5−2))/((−5+2)⋅(−5−2))
Simplify Numerator: Simplify the numerator.Now we distribute the 4 across the terms in the conjugate.4×(−5)+4×(−2)=−20−42
Simplify Denominator: Simplify the denominator.We use the difference of squares formula, which states that (a+b)(a−b)=a2−b2.(−5)2−(2)2= 25 - 2= 23
Write Simplified Expression: Write the simplified expression.Now we have the simplified numerator and denominator.(−20−42)/23This fraction is already in simplest form.
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