Question

If $\frac{3}{x}-\frac{2}{y}=5$ and $\frac{4}{x}-\frac{5}{y}=2$, then $\frac{1}{x}-\frac{1}{y}=?$

Where $(x,y\ne 0)$

• A. $1$
• B. $-1$
• C. $5$
• D. None of these

Answer 1

The correct option is A $1$

$\frac{3}{x}-\frac{2}{y}=5$ ........ eq(1)

$\frac{4}{x}-\frac{5}{y}=2$ ........ eq(2)

Multiply (1) by $-4$ and (2) by $3$ and add them

$-\frac{12}{x}+\frac{8}{y}=-20$ ...........eq(3)

$\frac{12}{x}-\frac{15}{y}=6$ .................eq(4)
adding eq(3) and eq(4)

$-\frac{7}{y}=-14\Rightarrow y=\frac{1}{2}$

Put $y=\frac{1}{2}$ in eq. (1)

$\frac{3}{x}-4=5\Rightarrow \frac{3}{x}=9\Rightarrow x=\frac{1}{3}$

$\frac{1}{x}=3$ and $\frac{1}{y}=2$

$\therefore$ $\frac{1}{x}-\frac{1}{y}=3-2=1$