The roots of 15/(x2 - 4) - 2/(x - 2) = 1 are……………… A) -

1.	The roots of 15/(x2 - 4) - 2/(x - 2) = 1 are……………… A) -3 and 5 B) 3 only C) -5 and 3 D) -5 only
Answer» Correct option is (C) -5 and 3 Given equation is \(\frac{15}{x^2-4}-\frac{2}{x-2}=1\) \(\Rightarrow\frac{15-2(x+2)}{x^2-4}=1\) \(\Rightarrow15-2x-4=x^2-4\) \(\Rightarrow x^2+2x-4+4-15=0\) \(\Rightarrow x^2+2x-15=0\) \(\Rightarrow x^2+5x-3x-15=0\) \(\Rightarrow x(x+5)-3(x+5)=0\) \(\Rightarrow(x+5)(x-3)=0\) \(\Rightarrow x+5=0\) \(or\;x-3=0\) \(\Rightarrow x=-5\;or\;x=3\) Hence, the roots of given equation are -5 and 3. Correct option is C) -5 and 3

The roots of 15/(x2 - 4) - 2/(x - 2) = 1 are……………… A) -3 and 5 B) 3 only C) -5 and 3 D) -5 only

Answer»

Correct option is (C) -5 and 3

Given equation is

\(\frac{15}{x^2-4}-\frac{2}{x-2}=1\)

\(\Rightarrow\frac{15-2(x+2)}{x^2-4}=1\)

\(\Rightarrow15-2x-4=x^2-4\)

\(\Rightarrow x^2+2x-4+4-15=0\)

\(\Rightarrow x^2+2x-15=0\)

\(\Rightarrow x^2+5x-3x-15=0\)

\(\Rightarrow x(x+5)-3(x+5)=0\)

\(\Rightarrow(x+5)(x-3)=0\)

\(\Rightarrow x+5=0\) \(or\;x-3=0\)

\(\Rightarrow x=-5\;or\;x=3\)

Hence, the roots of given equation are -5 and 3.

Correct option is C) -5 and 3