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Given that \(\dfrac{6 x+m}{2 x^{2}+7 x-15} \equiv \dfrac{4}{x+5}-\dfrac{2}{2 x-3}\), find the value of \(m\).

A. 20
B. 12
C. \(-10\)
D. \(-22\)
in Mathematics by Bronze Status (7,596 points) | 122 views

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Best answer

Correct Answer:

Option D


Explanation
Taking the LCM of the right hand side of the equation, we have
\[
\frac{4(2 x-3)-2(x+5)}{(x+5)(2 x-3)}=\frac{6 x+m}{2 x^{2}+7 x-15}
\]
Comparing the numerators, we have
\[
\begin{aligned}
&4(2 x-3)-2(x+5)=6 x+m \\
&8 x-12-2 x-10=6 x-22=6 x+m \\
&\Longrightarrow m=-22
\end{aligned}
\]

by Bronze Status (7,596 points)
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