Difference between revisions of "004 Sample Final A, Problem 6"

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(Created page with "<span class="exam"> Simplify.      <math>\frac{1}{3x + 6} - \frac{x}{x^2-4} + \frac{3}{x-2}</math>")
 
 
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<span class="exam"> Simplify. &nbsp;&nbsp;&nbsp;&nbsp; <math>\frac{1}{3x + 6} - \frac{x}{x^2-4} + \frac{3}{x-2}</math>
 
<span class="exam"> Simplify. &nbsp;&nbsp;&nbsp;&nbsp; <math>\frac{1}{3x + 6} - \frac{x}{x^2-4} + \frac{3}{x-2}</math>
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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
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! Foundations
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|-
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|How do you simplify <math>\frac{1}{x}+\frac{1}{x+2}</math> into one fraction?
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|-
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|Answer:
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|-
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|You need to get a common denominator. The common denominator is <math>x(x+2)</math>. So,
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|-
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|<math>\frac{1}{x}+\frac{1}{x+2}=\frac{x+2}{x(x+2)}+\frac{x}{x(x+2)}=\frac{2x+2}{x(x+2)}</math>.
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|}
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Solution:
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{| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
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! Step 1:
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|-
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|If we factor the denominators, we have <math>\frac{1}{3(x+2)} - \frac{x}{(x+2)(x-2)} + \frac{3}{x-2}</math>.
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|-
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|So, the common denominator of these three fractions is <math>3(x-2)(x+2)</math>.
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|}
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{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
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! Step 2:
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|-
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|So, we have <math>\frac{1}{3(x+2)} - \frac{x}{(x+2)(x-2)} + \frac{3}{x-2}=\frac{x-2}{3(x-2)(x+2)} - \frac{3x}{3(x+2)(x-2)} + \frac{3(3)(x+2)}{3(x+2)(x-2)}</math>.
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|}
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{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
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! Step 3:
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|-
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|Now, combining into one fraction, we have <math>\frac{x-2-3x+3(3)(x+2)}{3(x-2)(x+2)}=\frac{7x+16}{3(x-2)(x+2)} </math>
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|}
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{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
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! Final Answer:
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|-
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|<math>\frac{7x+16}{3(x-2)(x+2)} </math>
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|}
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[[004 Sample Final A|<u>'''Return to Sample Exam</u>''']]

Latest revision as of 15:58, 4 May 2015

Simplify.     

Foundations
How do you simplify into one fraction?
Answer:
You need to get a common denominator. The common denominator is . So,
.


Solution:

Step 1:
If we factor the denominators, we have .
So, the common denominator of these three fractions is .
Step 2:
So, we have .
Step 3:
Now, combining into one fraction, we have
Final Answer:

Return to Sample Exam

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