Problem 16

Question

Evaluate each algebraic expression for the given value or values of the variable(s). $$\frac{2 x+y}{x y-2 x}, \text { for } x=-2 \text { and } y=4$$

Step-by-Step Solution

Verified
Answer
The evaluated expression, given x = -2 and y = 4, is 0.
1Step 1: Substitute Given Values
Replace x and y in the expression \(\frac{2x+y}{xy-2x}\) with -2 and 4 respectively. This results in \(\frac{2(-2)+4}{(-2)(4)-2(-2)}\).
2Step 2: Simplify Numerator
The numerator of the fraction becomes -4+4 which equals 0.
3Step 3: Simplify Denominator
For the denominator, calculation becomes -8 + 4 which equals -4.
4Step 4: Finalize the Equation
The fraction becomes \(\frac{0}{-4}\) which simplifies to 0. Any number divided by a non-zero number will always be 0.