Question

Solve by factorising $\frac{1}{(x+4)}-\frac{1}{(x-7)}=\frac{11}{30}$ where $x$ is not equal to $-4,7$.

Answer 1

$\frac{1}{(x+4)}-\frac{1}{(x-7)}=\frac{11}{30}$

where $x$$\ne -4,7$

Let us take LCM on both the side we get

$\frac{x-7-x-4}{(x+4)(x-7)}=\frac{11}{30}$

$\frac{-11}{(x+4)(x-7)}=\frac{11}{30}$

By doing cross multiplication we get

$(x+4)(x-7)=-30$

Let us solve the equation we get

$$\begin{gathered} x^2–7x+4x–28=-30 \\ {x}^2–3x+2=0 \end{gathered}$$

By splitting the middle term above equation can be written as

$$\begin{gathered} x^2–2x–x+2=0 \\ x(x–2)-1(x–2)=0 \\ (x–2)(x–1)=0 \end{gathered}$$

$x=2,x=1$

∴ the solution of the expression is $x=2,1$