Sure, let's solve the equation step by step.
Given:
[tex]\[
\frac{4}{u-7} - \frac{6}{u-7} = 2
\][/tex]
First, combine the fractions on the left-hand side:
[tex]\[
\frac{4}{u-7} - \frac{6}{u-7} = \frac{4 - 6}{u-7}
\][/tex]
Simplify the numerator:
[tex]\[
\frac{4 - 6}{u-7} = \frac{-2}{u-7}
\][/tex]
So the equation becomes:
[tex]\[
\frac{-2}{u-7} = 2
\][/tex]
To eliminate the fraction, multiply both sides of the equation by [tex]\(u-7\)[/tex]:
[tex]\[
-2 = 2(u - 7)
\][/tex]
Next, distribute the 2 on the right-hand side:
[tex]\[
-2 = 2u - 14
\][/tex]
Now, solve for [tex]\(u\)[/tex]. Start by adding 14 to both sides:
[tex]\[
-2 + 14 = 2u
\][/tex]
Simplify:
[tex]\[
12 = 2u
\][/tex]
Finally, divide both sides by 2:
[tex]\[
\frac{12}{2} = u
\][/tex]
So we have:
[tex]\[
u = 6
\][/tex]
Therefore, the solution is:
[tex]\[
u = 6
\][/tex]
