PYQ important questions

Q. Solve for X : $\frac{4}{X} - \frac{5}{(2X + 3)} = 3$

Ans: Given equation is:

$\frac{4}{X} - \frac{5}{(2X + 3)} = 3$

∴ $\frac{4 (2 X + 3) - 5 X }{X (2X + 3)} = 3$

∴ 4 (2 X + 3) – 5 X = 3 X (2X + 3)

∴ 8 X + 12 – 5 X = 6 X ²+ 9 X

∴ 12 = 6 X ²+ 6 X

∴ 6 X ²+ 6 X – 12 = 0

∴ X ²+ X – 2 = 0

∴ X ²+ 2 X – X – 2 = 0

∴ X ( X + 2) – 1 (X + 2) = 0

∴ (X + 2) (X – 1) = 0

∴ X = 1 and X = – 2

Therefore values of X are 1 and – 2

Check: Let’s check our answers:

at X = 1 in LHS, equation will become: $\frac{4}{1} - \frac{5}{(2 (1) + 3)}$

= 4 – $\frac{5}{5}$ = 4 – 1 = 3

at X = – 2 in LHS, equation will become: $\frac{4}{- 2} - \frac{5}{(2 (- 2) + 3)}$

= – 2 – $\frac{5}{(- 4 + 3)}$ = – 2 + 5 = 3

Since values of LHS matches with given value on RHS, our both answers are correct.

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