Divide and Simplify : (t-3)/(t+2)÷(4t-12)/(t+1)
To divide and simplify the expression, we can follow these steps:
Step 1: Simplify each fraction individually.
The first fraction (t-3)/(t+2) is already simplified, so we can leave it as it is.
To simplify the second fraction (4t-12)/(t+1), we can factor the numerator and the denominator:
4t - 12 = 4(t - 3)
t + 1 = (t + 1)
So the second fraction simplifies to 4(t-3)/(t+1).
Step 2: Rewrite the division as multiplication.
To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction. So our expression becomes:
(t-3)/(t+2) * (t+1)/(4(t-3))
Step 3: Cancel out common factors.
In this step, we look for any common factors between the numerator and the denominator that can be canceled out. In this case, (t-3) is a common factor. So we can cancel it out:
(t-3)/(t+2) * (t+1)/(4(t-3))
= 1/(t+2) * (t+1)/4
Step 4: Multiply the fractions.
To multiply fractions, we multiply the numerators together and the denominators together:
1/(t+2) * (t+1)/4
= (t+1)/(4(t+2))
So the final simplified expression is: (t+1)/(4(t+2))