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Chapter 6: Problem 34

Evaluate the algebraic expression for the given value or values of the variables. \(\frac{2 x+y}{x y-2 x} ; \quad x=-2, y=4\)

Short Answer

Expert verified
Therefore, the given expression when evaluated for \(x=-2\) and \(y=4\) gives the result 0.

Step by step solution

01

Substitute variables with given values

Replace \(x\) with -2 and \(y\) with 4 in the expression, thereby the expression becomes \(\frac{2(-2)+4}{-2*4-2*(-2)}\).
02

Simplify the numerator and the denominator

By following the rules of the order of operations, in the numerator, calculate the multiplication first to get -4 and then add 4, yielding 0. In the denominator, calculate the multiplication -2*(-2) to get 4 and -2*4 to get -8. Then subtract -8 from 4 resulting in 12. Thus, the expression is now \(\frac{0}{12}\).
03

Simplify the entire expression

Dividing zero by any non-zero number will always result in zero. Hence, \(\frac{0}{12}\) equals 0.

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