Question

The number of roots of the equation \[\frac{(x + 2)(x - 5)}{(x - 3)(x + 6)} = \frac{x - 2}{x + 4}\] is 

Options

• 0

• 1

• 2

• 3

Answer 1

1

\[\frac{(x + 2) (x - 5)}{(x - 3) (x + 6)} = \frac{(x - 2)}{(x + 4)}\]

\[ \Rightarrow ( x^2 - 3x - 10) (x + 4) = ( x^2 + 3x - 18) (x - 2)\]

\[ \Rightarrow x^3 + 4 x^2 - 3 x^2 - 12x - 10x - 40 = x^3 - 2 x^2 + 3 x^2 - 6x - 18x + 36\]

\[ \Rightarrow x^2 - 22x - 40 = x^2 - 24x + 36\]

\[ \Rightarrow 2x = 76\]

\[ \Rightarrow x = 38\]

Hence, the equation has only 1 root.