Question

Simplify the rational expressions into lowest forms.

(i) $\frac{5x+20}{7x+28}$

(ii) $\frac{x^3-5x^2}{3x^3+2x^4}$

(iii) $\frac{6x^2-5x+1}{9x^2+12x-5}$

(iv) $\frac{(x-3)(x^2-5x+4)}{(x-1)(x^2-2x-3)}$

Answer 1

1. Now, $\frac{5x+20}{7x+28}=\frac{5(x+4)}{7(x+4)}=\frac{5}{7}$

2.Now, $\frac{x^3-5x^2}{3x^3+2x^4}=\frac{x^2(x-5)}{x^3(2x+3)}=\frac{x-5}{x(2x+3)}$

3.Let, $p\left(x\right)=6x^2-5x+1=(2x-1)(3x-1)$ and $q\left(x\right)=9x^2+12x-5=(3x+5)(3x-1)$Therefore, $\frac{p\left(x\right)}{q\left(x\right)}=\frac{(2x-1)(3x-1)}{(3x+5)(3x-1)}=\frac{2x-1}{3x+5}$

4.Let, $f\left(x\right)=(x-3)(x^2-5x+4)=(x-3)(x-1)(x-4)$ and

$g\left(x\right)=(x-1)(x^2-2x-3)=(x-1)(x-3)(x+1)$

Therefore, $\frac{f\left(x\right)}{g\left(x\right)}=\frac{(x-3)(x-1)(x-4)}{(x-1)(x-3)(x+1)}=\frac{x-4}{x+1}$