Can anyone help with this last question?
8v/v^2-49 + v/v-7
8/v + v/v - 49 -7 =
9/v - 56
Can you work it from there?
Simplify:
-3 · -u · -7v + 8v - 6uv
Certainly! Let's break down the expression step by step.
The expression you provided is:
8v/(v^2 - 49) + v/(v - 7)
To simplify this expression, we first need to factor the denominators.
The first denominator, v^2 - 49, is a difference of squares, which factors as (v + 7)(v - 7).
The second denominator, v - 7, cannot be factored further.
After factoring, we have:
8v/[(v + 7)(v - 7)] + v/(v - 7)
Now that we have the common denominator (v - 7), we can combine the fractions.
To do this, we need to find a common denominator for the numerators. Since the first numerator, 8v, does not have any common factors with v, we can leave it as is.
Now, we can combine the two fractions over the common denominator (v - 7):
[8v + v(v + 7)]/(v - 7)
Simplifying further:
[8v + v^2 + 7v]/(v - 7)
Combining like terms:
(v^2 + 15v)/(v - 7)
And that's our simplified expression!