Simplify (4M^2+7M-2)/(2M^2-8)*(1/(M-2))^-1

Problem

(4*M2+7*M−2)/(2*M2−8)⋅(1/(M−2))(−1)

Solution

1. Factor the quadratic trinomial in the numerator of the first fraction by finding two numbers that multiply to −8 and add to 7

4*M2+7*M−2=(4*M−1)*(M+2)

2. Factor the denominator of the first fraction by first pulling out the greatest common factor and then using the difference of squares formula.

2*M2−8=2*(M2−4)

2*(M2−4)=2*(M−2)*(M+2)

3. Simplify the second term by applying the negative exponent rule, which states that a(−1)=1/a

(1/(M−2))(−1)=M−2

4. Substitute the factored forms back into the original expression.

((4*M−1)*(M+2))/(2*(M−2)*(M+2))⋅(M−2)

5. Cancel the common factors (M+2) and (M−2) from the numerator and denominator.

(4*M−1)/2

Final Answer

(4*M2+7*M−2)/(2*M2−8)⋅(1/(M−2))(−1)=(4*M−1)/2

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