Question

Please solve and explain. Photo attached

Answer 1

$\frac{(x+1)(x-3)}{x^{2}}$

Solution:

Given expression:

$\frac{\frac{36}{x^{2}}+\frac{36}{x}}{\frac{36}{x-3}}$

To solve this expression:

$\frac{\frac{36}{x^{2}}+\frac{36}{x}}{\frac{36}{x-3}}$

Apply the fraction rule: $\frac{a}{\frac{b}{c}}=\frac{a \cdot c}{b}$

      $=\frac{\left(\frac{36}{x^{2}}+\frac{36}{x}\right)(x-3)}{36}$

Let us solve $\frac{36}{x^{2}}+\frac{36}{x}$.

Least common multiple of $x^{2}, x$ is $x^{2}$.

Make the denominator same based on the LCM.

So that multiply and divide the 2nd term by x, we get

$\frac{36}{x^{2}}+\frac{36}{x}=\frac{36}{x^{2}}+\frac{36 x}{x^{2}}$

              $=\frac{36+36 x}{x^{2}}$

Now, multiply by (x - 3).

$\frac{36+36 x}{x^{2}}(x-3)= \frac{(36 x+36)(x-3)}{x^{2}}$

$\frac{\left(\frac{36}{x^{2}}+\frac{36}{x}\right)(x-3)}{36}=\frac{\frac{(36 x+36)(x-3)}{x^{2}}}{36}$

Apply the fraction rule: $\frac{\frac{b}{c}}{a}=\frac{b}{c \cdot a}$

                            $=\frac{(36x+36)(x-3)}{x^{2} \cdot 36}$

                            $=\frac{36(x+1)(x-3)}{x^{2} \cdot 36}$

Cancel the common factor 36.

                            $=\frac{(x+1)(x-3)}{x^{2}}$

Hence the solution is $\frac{(x+1)(x-3)}{x^{2}}$.