SOLUTION: Write each rational expression as an equivalent expression with the indicated denominator. \frac{14}{z^2-3z}=\frac{?}{z\left(z-3\right)\left(z-2\right)}

Question 1201042: Write each rational expression as an equivalent expression with the indicated denominator.
\frac{14}{z^2-3z}=\frac{?}{z\left(z-3\right)\left(z-2\right)}
Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!

LHS = left hand side
RHS = right hand side

Let n be the unknown numerator expression in the RHS fraction.

n is some expression in terms of z.

Let's factor the denominator of the LHS.

This means

is the same as

The factors for the LHS denominator are z and (z-3). Both of which are present in the RHS denominator . The LHS denominator is missing the factor (z-2).

We'll multiply top and bottom of the LHS fraction by (z-2) to fill in that missing gap.

Both denominators of the LHS and RHS have the same exact factorization. The fractions are only equal if the numerators were the same. Therefore, we must have n = 14(z-2) = 14z-28

In other words,

after multiplying top and bottom by (z-2).

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