+142 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.
+6250 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.
