# How do you simplify #(2t^2+7t-4)/(-2t^2-5t+3)#?

##### 1 Answer

#### Answer:

#### Explanation:

Factorize first as described below:

**Factor by splitting the middle term**

**Step-1 : Multiply the coefficient of the first term by the constant # 2 xx -4 = -8#**

**Step-2 : Find two factors of #-8# whose sum equals the coefficient of the middle term, which is #7#.**

**Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, #-1# and # 8#**

Now lets do the same for

** Re-write the equation as #color(red)(-1(2t^2+5t-3))#**

**Factor by splitting the middle term**

**Step-1 : Multiply the coefficient of the first term by the constant #2 xx -3 = -6#**

**Step-2 : Find two factors of #-6# whose sum equals the coefficient of the middle term, which is #5# .**

**Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step #2# above, #-1# and #6#.**

So now we get: