Consider the expressions $\frac{4x^3+2x^2+6x+7}{2x+1}$ and $2x^2+3+\frac4{2x+1}.$ a) show that these expressions are equal when $x=10.$ b) explain why these expressions are not equal when $x=-\dfrac12.$ c) show that these expressions are equal for all $x$ other than $-\dfrac12.$ in parts (a) and (c), begin by explaining what your strategy for solving will be.

Part a)  In order to solve the equation, we will simplify both of them.  Once we do that, if we notice, they are the same equation, so therefore, if x=10, then we will be able to match the equation.

Part b) The reason the expressions are not equal when x=-1/2 is because if we see, that in the second expression, 2x^2, if x=-1/2, then the answer becomes -1, and we eventually end up with 1.

Part c)  As we can see, the expressions are the same, so if x is any number other than -1/2, then we will be able to show that the expressions are equal.

Step-by-step explanation:

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By the way, this question is from the Art of Problem Solving, and you should not just copy answers or copy of them.

c. (3,2,6) is the answer.

$15 each

step-by-step explanation:

$45/3 children= $15 each