Simplify: \(\frac{5}{x - y} - \frac{4}{y - x}\)
A
9/x - y
B
9/y - x
C
1/x - y
D
1/y - x
E
y - 9x/x - y
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\(\frac{5}{x - y} - \frac{4}{y - x}\)
= \(\frac{5(y - x) - 4(x - y)}{(x - y)(y - x)}\)
= \(\frac{5y - 5x - 4x + 4y}{(x - y)(y - x)}\)
= \(\frac{9y - 9x}{(x - y)(y - x)}\)
= \(\frac{9(y - x)}{(x - y)(y - x)}\)
= \(\frac{9}{x - y}\)
Source: Myschool Past Questions Archive (Record #23799)