Question

solve for v.\\(\frac{6v}{v - 7} - \frac{4}{v - 7} = 8\\)\
if there is more than one solution, separate them with commas.\
if there is no solution, click on
o solution\.

Explanation:

Step1: Combine the fractions

Since the denominators are the same ($v - 7$), we can combine the left - hand side fractions:
$\frac{6v-4}{v - 7}=8$

Step2: Multiply both sides by $v - 7$ (note that $v

eq7$ because the denominator cannot be zero)
We get $6v-4 = 8(v - 7)$

Step3: Expand the right - hand side

Using the distributive property $a(b + c)=ab+ac$, where $a = 8$, $b=v$ and $c=-7$, we have:
$6v-4=8v-56$

Step4: Move the $v$ terms to one side and constants to the other side

Subtract $6v$ from both sides:
$-4 = 2v-56$
Then add 56 to both sides:
$52 = 2v$

Step5: Solve for $v$

Divide both sides by 2:
$v = 26$

We need to check if $v = 26$ makes the original denominator zero. When $v = 26$, $v-7=26 - 7=19
eq0$, so it is a valid solution.

Answer:

26