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What is the value of (5x - 4y)/(2x - y)/(3y/(y-2x) + 5)

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Carcass
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What is the value of (5x - 4y)/(2x - y)/(3y/(y-2x) + 5) [#permalink] New post   11 Jan 2022, 07:28
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\(2x \neq y\)

\(5x \neq 4y\)

What is the value of \(\frac{\frac{5x-4y}{2x-y}}{\frac{3y}{y-2x} + 5}\) ?

A. \(\frac{1}{2}\)

B. \(\frac{3}{2}\)

C. \(\frac{5}{2}\)

D. \(\frac{7}{2}\)

E. \(\frac{9}{2}\)
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A
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Re: What is the value of (5x - 4y)/(2x - y)/(3y/(y-2x) + 5) [#permalink] New post   11 Jan 2022, 07:50
Carcass wrote:
\(2x \neq y\)

\(5x \neq 4y\)

What is the value of \(\frac{\frac{5x-4y}{2x-y}}{\frac{3y}{y-2x} + 5}\) ?

A. \(\frac{1}{2}\)

B. \(\frac{3}{2}\)

C. \(\frac{5}{2}\)

D. \(\frac{7}{2}\)

E. \(\frac{9}{2}\)

Key concept: It's important to recognize that the question is really asking us "What is the value of the expression for ALL values of x and y (except the exclusions noted)?"

So let's see what the expression evaluates to when x = 1 and y = 1..

\(\frac{\frac{5x-4y}{2x-y}}{\frac{3y}{y-2x} + 5}=\frac{\frac{5(1)-4(1)}{2(1)-(1)}}{\frac{3(1)}{(1)-2(1)} + 5}\)

\(=\frac{\frac{1}{1}}{\frac{3}{-1} + 5}\)

\(= \frac{1}{2}\)

Answer: A
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Re: What is the value of (5x - 4y)/(2x - y)/(3y/(y-2x) + 5) [#permalink] New post   08 Sep 2022, 10:55
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\(\frac{\frac{5x-4y}{2x-y}}{\frac{3y}{y-2x} + 5}\)

Multiplying both numerator and denominator of \(\frac{3y}{y-2x}\) by -1 we get

= \(\frac{\frac{5x-4y}{2x-y}}{\frac{-3y}{2x - y} + 5}\)

= \(\frac{\frac{5x-4y}{2x-y}}{\frac{-3y + 5*(2x-y)}{2x - y}}\) = \(\frac{5x-4y}{-3y + 5*(2x-y)}\)

= \(\frac{5x-4y}{-3y + 10x - 5y}\) = \(\frac{5x-4y}{-8y + 10x}\) = \(\frac{5x-4y}{2*(5x - 4y)}\) = \(\frac{1}{2}\)

So, Answer will be A
Hope it helps!
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Re: What is the value of (5x - 4y)/(2x - y)/(3y/(y-2x) + 5) [#permalink]
08 Sep 2022, 10:55
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