Question

Help please? I don't understand.

Answer 1

Given Equation:-

$\boxed{ \tt \frac{3}{x + 5} - \frac{2}{x - 3}}$

Step by step expansion:

$\dashrightarrow\sf\dfrac{3}{x + 5} - \dfrac{2}{x - 3}$

Write the equation

$\dashrightarrow\sf\dfrac{\frac{3 \times (x + 5)(x - 3)}{x + 5} - \frac{2 \times (x + 5)(x - 3)}{x - 3}}{(x + 5)(x - 3)}$

Take the lcm of the equation I.e (x + 5) (x + 3)

$\dashrightarrow\sf\dfrac{\frac{3 \times \cancel{(x + 5)}(x - 3)}{\cancel{x + 5}} - \frac{2 \times (x + 5)\cancel{(x - 3)}}{\cancel{x - 3}}}{(x + 5)(x - 3)}$

cancel like terms I.e (x + 5) with (x+ 5) and (x - 3) with (x - 3)

$\dashrightarrow\sf\dfrac{\frac{3 \times (x - 3)}{1} - \frac{2 \times (x + 5)}{1}}{(x + 5)(x - 3)}$

$\dashrightarrow\sf\dfrac{3 \times (x - 3)- 2 \times (x + 5)}{(x + 5)(x - 3)}$

Remove 1 as denominator

$\dashrightarrow\sf\dfrac{3x - 9- 2 (x + 5)}{(x + 5)(x - 3)}$

Multiply 3 with x - 9

$\dashrightarrow\sf\dfrac{3x - 9- 2 x - 10}{(x + 5)(x - 3)}$

Multiply - 2 with x + 5

$\dashrightarrow\sf\dfrac{3x - 2x- 9 - 10}{(x + 5)(x - 3)}$

Arrange the equation so that it would be easier to solve.

$\dashrightarrow\sf\dfrac{x- 9 - 10}{(x + 5)(x - 3)}$

Subtract 3x with 2x

$\dashrightarrow\bf\dfrac{x-19}{(x + 5)(x - 3)}$

Add -9 with - 10

$\therefore \underline {\textsf{\textbf{Option \red{one} is correct}}}$