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vesna_86 [32]
3 years ago
11

What is the simplified form of (x+9)/8 minus (x+3)/(x+2)?

Mathematics
2 answers:
Murrr4er [49]3 years ago
6 0
Here is the work to help you understand the problem.
\frac{x+9}{8}-\frac{x+3}{x+2}

\mathrm{Find\:the\:least\:common\:denominator\:} \ \textgreater \  8\left(x+2\right)

\mathrm{Adjust\:Fractions\:based\:on\:the\:LCD} \ \textgreater \  \frac{\left(x+9\right)\left(x+2\right)}{8\left(x+2\right)}-\frac{\left(x+3\right)\cdot \:8}{8\left(x+2\right)}

\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}: \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}

\frac{\left(x+9\right)\left(x+2\right)-8\left(x+3\right)}{8\left(x+2\right)}

Expand \left(x+9\right)\left(x+2\right)-8\left(x+3\right)

\left(x+9\right)\left(x+2\right)
\mathrm{Distribute\:parentheses\:using}: \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd
Where\; a=x,\:b=9,\:c=x,\:d=2

x\cdot \:x+x\cdot \:2+9\cdot \:x+9\cdot \:2 \ \textgreater \  \mathrm{Add\:similar\:elements:}\:2x+9x=11x

xx+11x+2\cdot \:9 \ \textgreater \  \mathrm{Apply\:exponent\:rule}: \:a^b\cdot \:a^c=a^{b+c}

xx=\:x^{1+1}=\:x^2 \ \textgreater \  x^2+11x+2\cdot \:9 \ \textgreater \  \mathrm{Multiply\:the\:numbers:}\:9\cdot \:2=18

x^2+11x+18 \ \textgreater \  x^2+11x+18-8\left(x+3\right)

-8\left(x+3\right) \ \textgreater \  \mathrm{Distribute\:parentheses\:using}: \:a\left(b+c\right)=ab+ac
Where\;a=-8,\:b=x,\:c=3

-8\cdot \:x-8\cdot \:3 \ \textgreater \  \mathrm{Multiply\:the\:numbers:}\:8\cdot \:3=24 \ \textgreater \  -8x-24

x^2+11x+18-8x-24 \ \textgreater \  \mathrm{Group\:like\:terms} \ \textgreater \  x^2+11x-8x+18-24

\mathrm{Add\:similar\:elements:}\:11x-8x=3x \ \textgreater \  x^2+3x+18-24

\mathrm{Add/Subtract\:the\:numbers:}\:18-24=-6 \ \textgreater \  x^2+3x-6

\frac{x^2+3x-6}{8\left(x+2\right)}

Hope this helps!
matrenka [14]3 years ago
5 0
The simplified form of (x+9)/8 - (x+3)/(x+2) is:

x^2+3x-6 over 8 (x+2)

Work:

1. (x+9)(x+2) - (x+3) x 8 over 8 (x+2)

2. (x+9)(x+2) - 8(x+3) over 8(x+2)

3. x^2 + 2x + 9x + 18 - 8x -24 over 8(x+2)

4. x^2 + (2x + 9x - 8x) + (18 - 24) over 8(x+2)

= x^2+3x-6 over 8 (x+2)

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