Question

simplify the question​

Answer 1

Question

Simplify

$\sf{\frac{12t^2-22t+8}{3t}\div \frac{3t^2+2t-8}{2t^2+4t}}$

Solution

Factorizing 12 t² - 22 t + 8

$\implies\sf{12t^2-22t+8}$

splitting middle term

$\implies\sf{12t^2-16t-6t+8}\\\implies\sf{4t(3t-4)-2(3t-4)}\\\underline{\underline{\implies\sf{(4t-2)(3t-4)}}...eqn(1)}$

Factorizing 3 t² + 2 t - 8

$\implies\sf{3t^2+2t-8}$

splitting middle term

$\implies\sf{3t^2+6t-4t-8}\\\implies\sf{3t(t+2)-4(t+2)}\\\underline{\underline{\implies\sf{(3t-4)(t+2)}}...eqn(2)}$

Now moving to the given expression

$\longmapsto\sf{\frac{12t^2-22t+8}{3t}\div \frac{3t^2+2t-8}{2t^2+4t}}$

It can be written as

$\longmapsto\sf{\frac{12t^2-22t+8}{3t}\times\frac{2t^2+4t}{3t^2+2t-8}}$

Using eqn (1) and (2)

$\longmapsto\sf{\frac{(4t-2)(3t-4)}{3t}\times\frac{2t(t+2)}{(3t-4)(t+2)}}$

On simplifying

$\longmapsto\sf{\frac{(4t-2)2}{3}}\\\\\longmapsto\boxed{\sf{\frac{8t-4}{3}}}$

Answer .