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If x is 2 greater than the reciprocal of y+2, then what the value of y
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29 Jul 2019, 10:07
29 Jul 2019, 10:07
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If x is 2 greater than the reciprocal of y+2, then what the value of y in terms of x?
A) \(\frac{5+2x}{2-x}\)
B) \(\frac{5+2x}{x-2}\)
C) \(\frac{5-2x}{x-2}\)
D) \(\frac{5-2x}{2+x}\)
E) \(\frac{5x+2}{2-x}\)
A) \(\frac{5+2x}{2-x}\)
B) \(\frac{5+2x}{x-2}\)
C) \(\frac{5-2x}{x-2}\)
D) \(\frac{5-2x}{2+x}\)
E) \(\frac{5x+2}{2-x}\)
Re: If x is 2 greater than the reciprocal of y+2, then what the value of y
[#permalink]
29 Jul 2019, 10:47
29 Jul 2019, 10:47
X-2 = 1/(Y+2)
Y+2 = 1/(X-2)
Y = (1/(X-2)) - 2
Y = (1-2X+4)/(X-2)
Y = (5-2X)/(X-2)
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Y+2 = 1/(X-2)
Y = (1/(X-2)) - 2
Y = (1-2X+4)/(X-2)
Y = (5-2X)/(X-2)
Posted from my mobile device
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Re: If x is 2 greater than the reciprocal of y+2, then what the value of y
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29 Jul 2019, 10:54
29 Jul 2019, 10:54
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x = \(\frac{1}{y+2}\) + 2, we want y in terms of x
\(\frac{1}{y+2}\) = x-2 ==> y+2 = \(\frac{1}{x-2}\) ==> y = \(\frac{1}{x-2}\) - 2 ==> \(\frac{1}{x-2}\) - \(\frac{2(x-2)}{x-2}\) ==> y = \(\frac{1-2x+4}{x-2}\) ==> y = \(\frac{5-2x}{x-2}\)
Therefore, the answer is C
\(\frac{1}{y+2}\) = x-2 ==> y+2 = \(\frac{1}{x-2}\) ==> y = \(\frac{1}{x-2}\) - 2 ==> \(\frac{1}{x-2}\) - \(\frac{2(x-2)}{x-2}\) ==> y = \(\frac{1-2x+4}{x-2}\) ==> y = \(\frac{5-2x}{x-2}\)
Therefore, the answer is C
