Fraction Question

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Fraction Question

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How would I express (2x - 1) / (x + 2) as A + B / (x+2), where A and B are integers?

I can do 2x / (x + 2) - 1 / (x+2) of course, but that doesn't work...

Any ideas?

EDIT: Sorry if I wasn't clear, but it's NOT:

${\frac{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}{\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right)}} = {\mathtt{A}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{B}}}{\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right)}}$

But instead I need to change:

${\frac{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}{\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right)}}$

Into something that looks like:

${\mathtt{A}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{B}}}{\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right)}}$

Thank you!

Will85237 Jan 19, 2015

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I think anon's logic should work but I would do it much more simply.

$\frac{2x-1 }{ x+2}\\\\ =\frac{2(x+2)-1-4}{x+2}\\\\ =\frac{2(x+2)-5}{x+2}\\\\ =\frac{2(x+2)}{x+2}+\frac{-5}{x+2}\\\\ =2+\frac{-5}{x+2}$

Don't give anon negative points for trying to help you!!!

Melody Jan 19, 2015

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Melody · Answer 1 · 2015-01-19T04:37:59

I think anon's logic should work but I would do it much more simply.

$\frac{2x-1 }{ x+2}\\\\ =\frac{2(x+2)-1-4}{x+2}\\\\ =\frac{2(x+2)-5}{x+2}\\\\ =\frac{2(x+2)}{x+2}+\frac{-5}{x+2}\\\\ =2+\frac{-5}{x+2}$

Don't give anon negative points for trying to help you!!!

Guest · Answer 2 · 2015-01-19T04:17:30

Start by multiplying both sides by (x+2), giving 2x-1 = A(x+2)+B

Now, multiply out and equate x terms on the left to x terms on the right, and we have A=2, and also -1=2A+B

Now just solve for B. 🚲

Melody · Answer 3 · 2015-01-19T04:59:45

YES anon understood what you wanted and gave you a correct answer!

I shall show you

$\\\frac{2x-1}{x+2}=A+\frac{B}{x+2}\\\\ $multiply both sides by (x+2)$\\ 2x-1=A(x+2)+B\\ 2x-1=Ax+2A+B\\ 2x-1=Ax+(2A+B)\\ $ equating co-efficients$\\ 2=A\\ -1=2A+B\\ -1=4+B\\ B=-5\\ so\\ \frac{2x-1}{x+2}=2+\frac{-5}{x+2}\\\\$

so maybe you owe anon an appology

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Start by multiplying both sides by (x+2), giving 2x-1 = A(x+2)+B

Now, multiply out and equate x terms on the left to x terms on the right, and we have A=2, and also -1=2A+B

Now just solve for B. 🚲

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Start by multiplying both sides by (x+2), giving 2x-1 = A(x+2)+B

Now, multiply out and equate x terms on the left to x terms on the right, and we have A=2, and also -1=2A+B

Now just solve for B. 🚲

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