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(5m^(2)+7m)/(2m-9)-(2m)/(2m-9)
Which expression is equivalent to the difference?
Choose 1 answer:
(A)
(3m^(2)+7m)/(2m-9)
(B)
(5m^(2)+5m)/(2m-9)
(C)
(5m+9m)/(2m-9)
(D)
(5m^(2)+7m-1)/(2m-9)

$\frac{5 m^{2}+7 m}{2 m-9}-\frac{2 m}{2 m-9}$ $\newline$ Which expression is equivalent to the difference? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{3 m^{2}+7 m}{2 m-9}$ $\newline$ (B) $\frac{5 m^{2}+5 m}{2 m-9}$ $\newline$ (C) $\frac{5 m+9 m}{2 m-9}$ $\newline$ (D) $\frac{5 m^{2}+7 m-1}{2 m-9}$

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Compare linear and exponential growth

Full solution

Q.

\frac{5 m^{2}+7 m}{2 m-9}-\frac{2 m}{2 m-9}

\newline

Which expression is equivalent to the difference?

\newline

Choose

1

answer:

\newline

(A)

\frac{3 m^{2}+7 m}{2 m-9}

\newline

(B)

\frac{5 m^{2}+5 m}{2 m-9}

\newline

(C)

\frac{5 m+9 m}{2 m-9}

\newline

(D)

\frac{5 m^{2}+7 m-1}{2 m-9}

Write and identify common denominator: Write down the given expressions and identify the common denominator. $\newline$ The given expressions are $(5m^2 + 7m) / (2m - 9)$ and $(2m) / (2m - 9)$ . The common denominator is $(2m - 9)$ .
Combine expressions over common denominator: Combine the expressions over the common denominator. $\newline$ Since the denominator is the same for both expressions, we can combine the numerators over the common denominator: $\newline$ $\left(5m^2 + 7m\right) - \left(2m\right)$ / $2m - 9$ .
Subtract numerators: Subtract the numerators. $\newline$ Subtract $2m$ from $(5m^2 + 7m)$ to get: $\newline$ $\frac{5m^2 + 7m - 2m}{2m - 9}$ .
Simplify numerator: Simplify the numerator. $\newline$ Combine like terms in the numerator: $\newline$ $(5m^2 + 5m) / (2m - 9)$ .
Match simplified expression with choices: Match the simplified expression with the given choices. $\newline$ The simplified expression $(5m^2 + 5m) / (2m - 9)$ matches choice (B).

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