Try to simplify the following rational expression: Class 9

Try to simplify the following rational expression: Class 9

Question 1.

Try to simplify the following rational expression: Class 9

$\frac{36 s^2-12 s t+t^2}{t^2+2 t s-48 s^2}=\frac{(6 s-t)^2}{(++)(++)}$

(Hint: Factor t² + 2ts - 48s² and simplify the rational expressions assuming that t² + 2ts - 48s² ≠ 0)

Answer:

t² + 2ts - 48s²

Find two numbers a and b such that a + b = 2 and ab = -48

Since 8 + (- 6) = 2 and 8 × (- 6) = - 48,

the two numbers are 8 and - 6.

t² + 2ts - 48s² = (t + 8s)(t - 6s)

$\frac{36 s^2-12 s t+t^2}{t^2+2 t s-48 s^2}=\frac{(6 s-t)^2}{(t+8 s)(t+(-6 s))}$