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What is the value of (5x - 4y)/(2x - y)/(3y/(y-2x) + 5)
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11 Jan 2022, 07:28
11 Jan 2022, 07:28
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Question Stats:
85% (01:50) correct
14% (03:54) wrong based on 27 sessions
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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. \(\frac{9}{2}\)
\(5x \neq 4y\)
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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Re: What is the value of (5x - 4y)/(2x - y)/(3y/(y-2x) + 5)
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11 Jan 2022, 07:50
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. \(\frac{9}{2}\)
\(5x \neq 4y\)
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)
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08 Sep 2022, 10:55
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!
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!
