Question

solve for x:- [x²-9] / [x+3] = 4/7​

Answer 1

$\textsf{\large{\underline{Solution}:}}$

We have to solve the given equation for x ≠ -3.

Given that:

$\rm: \longmapsto \dfrac{ {x}^{2} - 9}{x + 3} = \dfrac{4}{7}$

We know that:

$\rm: \longmapsto {x}^{2} - {y}^{2} = (x + y)(x - y)$

Therefore, we get:

$\rm: \longmapsto \dfrac{ {x}^{2} - {3}^{2} }{x + 3} = \dfrac{4}{7}$

$\rm: \longmapsto \dfrac{(x + 3)(x - 3)}{(x + 3)} = \dfrac{4}{7}$

We can cancel out (x + 3) as x ≠ 3. We get:

$\rm: \longmapsto x - 3 = \dfrac{4}{7}$

Adding 3 to both sides, we get:

$\rm: \longmapsto x = 3 \dfrac{4}{7}$

Therefore:

$\rm: \longmapsto x = 3 \dfrac{4}{7} \: \: \: (Answer)$

$\textsf{\large{\underline{Verification}:}}$

Put x = 25/7 in the expression, we get:

$\rm = \dfrac{ \bigg( \dfrac{25}{7} \bigg)^{2} - {9}^{2} }{ \dfrac{25}{7} + 3 }$

$\rm = \dfrac{ \bigg( \dfrac{25}{7} + 3\bigg) \cdot \bigg( \dfrac{25}{7} - 3 \bigg)}{ \bigg( \dfrac{25}{7} + 3 \bigg)}$

$\rm = \dfrac{25}{7} - 3$

$\rm = \dfrac{25 - 21}{7}$

$\rm = \dfrac{4}{7}$

★ Hence, our answer is correct (Verified)