Use the following expression to answer the questions below:
(1/x+3 + 6/x^2+4x+3)*x+3/x+1

a. Simplify the expression down to one rational expression.
b. Explain the steps you used to do the simplification.
c. Are there any values x cannot be? Explain.
d. Find the values of x that make the expression equal to 0. Explain the steps you used to find these values.

Question

09-08-2017
Mathematics

contestada

Use the following expression to answer the questions below:
(1/x+3 + 6/x^2+4x+3)*x+3/x+1

a. Simplify the expression down to one rational expression.
b. Explain the steps you used to do the simplification.
c. Are there any values x cannot be? Explain.
d. Find the values of x that make the expression equal to 0. Explain the steps you used to find these values.

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eco92 eco92 · Answer 1 · 2017-08-14T13:13:44+02:00

We want to simplify:

[tex] (\frac{1}{x+3}+ \frac{6}{ x^{2} +4x+3})* \frac{x+3}{x+1} [/tex]

first we factorize [tex]x^{2} +4x+3[/tex] as [tex](x+3)(x+1)[/tex]

then multiply [tex]\frac{1}{x+3}[/tex] by [tex] \frac{x+1}{x+1} [/tex] to equalize the denominators of the first expression, and add the fractions.

[tex](\frac{1}{x+3}*\frac{x+1}{x+1} + \frac{6}{(x+3)(x+1)})* \frac{x+3}{x+1} [/tex]
[tex]\frac{x+7}{(x+3)(x+1)}* \frac{x+3}{x+1}[/tex]

simplify x+3:

[tex]\frac{x+7}{(x+1)}* \frac{1}{x+1}= \frac{x+7}{ x^{2} +2x+1} [/tex]

a.
[tex]\frac{x+7}{ x^{2} +2x+1}[/tex]

b.
steps already described

c.
x cannot be -1, nor -3 because the fractions with denominators (x+1) and (x+3) would not be defined.