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Consider the expressions  $$\frac{4x^3+2x^2+6x+7}{2x+1}$$and  $$2x^2+3+\frac{4}{2x+1}$$

a) Show that these expressions are equal when $$x=10$$

b) Explain why these expressions are not equal when $$x=-\frac{1}{2}$$

c) Show that these expressions are equal for all $$x$$ other than $$-\frac{1}{2}$$

In parts (a) and (c), begin by explaining what your strategy for solving will be.

Jun 9, 2019
edited by KeyLimePi  Jun 9, 2019

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a) I assume you can plug 10 into both expressions and evaluate them.  Actually, as the denominators are identical.

you only have to evaluate the numerators at x=10.  Do it and show they are equal at x=10.

b) what do you get in the denominator of both expressions when x = -1/2.  Are we allowed to divide by this number?

c) here you have a bit of algebra to do.  You need to convert the right hand side to an equivalent fraction with (2x+1) in the denominator.

Then you will see that the resulting numerators are the same.

Jun 9, 2019