Problem 16 - College Algebra Essentials

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

Answer

The evaluated value of the expression for \(x=-2\) and \(y=4\) is 0.

Step 1: Substitute the given values into the expression

Replace \(x\) with \(-2\) and \(y\) with \(4\) in the expression \(\frac{2 x+y}{x y-2 x}\). This results in: \(\frac{2 (-2)+4}{(-2)(4)-2(-2)}\).

Step 2: Simplify the expression

Perform the operations in the numerator and the denominator separately. In the numerator, 2*(-2) + 4 equals -4 + 4, which equals to 0. In the denominator, (-2)*(4) - 2*(-2) equals -8 + 4, which is -4. So we get \(\frac{0}{-4}\).

Step 3: Division by nonzero number

The value of a number divided by a non-zero number is zero. A nonzero number multiplied by zero equals zero. Hence, our final expression \(\frac{0}{-4}\) equals to 0.