Question

Evaluate the algebraic expression StartFraction 5 x plus y Over xy minus 5 x EndFraction
for xequalsnegative 1 and yequals3.

Simplify your answer.

Answer 1

To evaluate the expression \(\frac{5x + y}{xy - 5x}\) for \(x = -1\) and \(y = 3\), we will first substitute these values into the expression.

1. Substitute \(x = -1\) and \(y = 3\):
\[
\frac{5(-1) + 3}{(-1)(3) - 5(-1)}
\]

2. Calculate the numerator:
\[
5(-1) + 3 = -5 + 3 = -2
\]

3. Calculate the denominator:
\[
(-1)(3) - 5(-1) = -3 + 5 = 2
\]

4. Now substitute the values back into the expression:
\[
\frac{-2}{2}
\]

5. Simplify:
\[
\frac{-2}{2} = -1
\]

Therefore, the value of the expression \(\frac{5x + y}{xy - 5x}\) for \(x = -1\) and \(y = 3\) is \(-1\).