Solve for x : 16/x − 1 = 15/(x + 1)
Question
Solve for x:
\[ \frac{16}{x}-1=\frac{15}{x+1}, \qquad x\ne0,-1 \]Solution
Multiplying both sides by \(x(x+1)\),
\[ 16(x+1)-x(x+1)=15x \]
\[ 16x+16-x^2-x=15x \]
\[ -x^2+16=0 \]
\[ x^2-16=0 \]
\[ (x-4)(x+4)=0 \]
\[ x=4 \]
or
\[ x=-4 \]
Both values satisfy the given restrictions.
Answer
\[
\boxed{x=4 \quad \text{or} \quad x=-4}
\]