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Chapter 6: Problem 33

Evaluate the algebraic expression for the given value or values of the variables. \(\frac{2 x+3 y}{x+1} ; \quad x=-2, y=4\)

Short Answer

Expert verified
The algebraic expression \(\frac{2 x + 3 y}{x + 1}\), evaluated at \(x=-2\) and \(y=4\), is \(-8\).

Step by step solution

01

Plug the Values into the Expression

Start by substituting the given values of \(x=-2\) and \(y=4\) into the algebraic expression \(\frac{2 x + 3 y}{x + 1}\). This gives us \(\frac{2(-2) + 3(4)}{-2 + 1}\).
02

Simplify the Numerator

The expression in the numerator of the fraction simplifies as follows: \(2(-2) + 3(4) = -4 + 12 = 8\). Therefore, our expression now reads \(\frac{8}{-2 + 1}\).
03

Simplify the Denominator

The expression in the denominator simplifies as follows: \(-2 + 1 = -1\). Substituting this into our fraction, we get \(\frac{8}{-1}\).
04

Simplify the Final Expression

This results in the fraction \(\frac{8}{-1}\) simplifying to \(-8\).

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