Question

Solve for x and simplify the answer fully.
start fraction, x, plus, 7, divided by, x, plus, 1, end fraction, equals, start fraction, 6, divided by, 7, end fraction
x+1
x+7
​
=
7
6

Answer 1

\(\dfrac{x+7}{x+1}=\dfrac{6}{7}\)

Cross-multiply: \(7(x+7)=6(x+1)\).

So \(7x+49=6x+6\Rightarrow x=6-49=-43\).

Domain: \(x\neq -1\), so \(x=-43\) is valid.

Answer: \(-43\).