_m^2 -1___ * _2m -2____ =
(m – 1)^2 3m + 3
Actually my computer won't allow the line and these are like fractions.
m^2 - 1/(m-1)^2 * 2m - 2/3m +3 =
I am having a problem trying to follow the steps to show my work and come out with the correct answer. Thanks.
To simplify the given expression, follow these steps:
Step 1:
Start by factoring the denominator of the first fraction, (m – 1)^2, to get m^2 - 2m + 1.
Step 2:
Now, multiply both the numerator and denominator of the first fraction by the conjugate of the denominator, which is m^2 - 2m + 1. This will help simplify the expression, removing any complex fractions.
So we get:
(m^2 - 1) * (2m - 2) / (m - 1)^2 * (3m + 3)
= [(m^2 - 1)(2m - 2)] / [(m - 1)(m - 1)(3m + 3)]
Step 3:
Next, simplify each factor in the numerator and denominator.
In the numerator, you can use the difference of squares formula:
(m^2 - 1)(2m - 2) = [(m - 1)(m + 1)(2)(m - 1)]
= 2(m - 1)(m + 1)(m - 1)
In the denominator, note that (m - 1)(m - 1) can be rewritten as (m - 1)^2, and 3m + 3 can be factored out as 3(m + 1).
So, the expression becomes:
2(m - 1)(m + 1)(m - 1) / (m - 1)^2 * 3(m + 1)
= 2(m + 1)(m - 1) / (m - 1)(m - 1) * 3(m + 1)
Step 4:
Now, cancel out common factors in the numerator and denominator.
Cancelling out (m - 1)(m + 1) from both the numerator and denominator, we're left with:
2 / (m - 1) * 3
= 6 / (m - 1)
Therefore, the simplified expression is 6 / (m - 1).
Remember to always check for any restrictions on the variable m, as division by zero is not defined. In this case, the expression is undefined when m = 1, as it would result in division by zero.