Chapter SH, Problem 8.17EP

To determine

To find: the solution of the equation and verify it.

Answer to Problem 8.17EP

At $\text{x=8}$ is solution of the equation which is verified.

Explanation of Solution

Given:

  $\frac{\text{12}}{\text{x+4}}\text{-}\frac{\text{3}}{\text{x-3}}\text{=}\frac{\text{24}}{{\text{x}}^{\text{2}}\text{+x-12}}$ .

Concept used:

Here the denominator is taken common by taking lowest common multiple.

The solution can be verified by putting the value of $\text{x}$ back to the equation and when $\text{L}\text{.HS=R}\text{.HS}$ The equation is verified.

Calculation:

  $\frac{\text{12}}{\text{x+4}}\text{-}\frac{\text{3}}{\text{x-3}}\text{=}\frac{\text{24}}{{\text{x}}^{\text{2}}\text{+x-12}}$ ........... $\left(\text{i}\right)$

  $\Rightarrow \frac{\text{12}\left(\text{x-3}\right)-3\left(\text{x+4}\right)}{\left(\text{x+4}\right)\left(\text{x-3}\right)}\text{=}\frac{\text{24}}{{\text{x}}^{\text{2}}\text{+4x-3x-12}}$ .

  $\Rightarrow \frac{\text{12}\left(\text{x-3}\right)\text{-3}\left(\text{x+4}\right)}{\left(\text{x+4}\right)\left(\text{x-3}\right)}\text{=}\frac{\text{24}}{\text{x}\left(\text{x+4}\right)\text{-3}\left(\text{x+4}\right)}$ .

  $\Rightarrow \frac{\text{12}\left(\text{x-3}\right)\text{-3}\left(\text{x+4}\right)}{\left(\text{x+4}\right)\left(\text{x-3}\right)}\text{=}\frac{\text{24}}{\left(\text{x-3}\right)\left(\text{x+4}\right)}$ .

By cross multiplying the equation:

  $\text{12}\left(\text{x-3}\right)\text{-3}\left(\text{x+4}\right)\text{=24}\text{.}$

  $\Rightarrow \text{12x-36-3x-12=24}\text{.}$

  $\Rightarrow \text{9x=24+48}$ .

  $\Rightarrow \text{9x=72}$ .

The value of $\text{x=8}$ .

By putting the value of $\text{x=8}$ in equation $\left(\text{i}\right)$ :

  $\frac{\text{12}}{\left(8\right)\text{+4}}\text{-}\frac{\text{3}}{\left(8\right)\text{-3}}\text{=}\frac{\text{24}}{{\left(8\right)}^{\text{2}}\text{+}\left(8\right)\text{-12}}$ .

  $\Rightarrow \frac{\text{12}}{\left(8\right)\text{+4}}\text{-}\frac{\text{3}}{\left(8\right)\text{-3}}\text{=}\frac{\text{24}}{{\left(8\right)}^{\text{2}}\text{+}\left(8\right)\text{-12}}$ .

  $\Rightarrow \frac{\text{12}}{12}\text{-}\frac{\text{3}}{5}\text{=}\frac{\text{24}}{60}$ .

  $\Rightarrow \frac{\text{12}\times \text{5-3}\times \text{12}}{12\times 5}\text{=}\frac{\text{24}}{60}$ .

  $\Rightarrow \frac{60\text{-}36}{60}\text{=}\frac{\text{24}}{60}$ .

  $\Rightarrow \frac{24}{60}\text{=}\frac{\text{24}}{60}$ .

  $\text{L}\text{.HS=R}\text{.HS}$ .

Hence, at $\text{x=8}$ is solution of the equation which is verified.