Question

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

Answer 1

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)

Answer 2

Here is the work to help you understand the problem.

`(x+9)/(8)-(x+3)/(x+2)`


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


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


`\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}: (a)/(c)\pm (b)/(c)=(a\pm \:b)/(c)`


`(\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`


`(x^2+3x-6)/(8\left(x+2\right))`

Hope this helps!