Q)$\displaystyle
\frac{6a^2+5a-6}{3a-2}
$
Q)$\displaystyle \frac{5b^3+7b^2+12}{b+2}$
Please answer the following in steps..
Thank you
To simplify, start by factoring the numerator:
$\displaystyle 6a^2+5a-6 = (3a-2)(2a+3)$
Which gives us:
$\displaystyle \frac{(3a-2)(2a+3)}{(3a-2)}$
Cancel out the common term:
$\displaystyle 2a+3$
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For the 2nd question, you can use long division. I'm not sure about the LaTeX, but it works the same as long division with integers.
If you need to see it, this is a good tutorial: http://www.purplemath.com/modules/polydiv2.htm
Hello, mj.alawami!
Just factor and reduce . . .
$\displaystyle \frac{6a^2+5a-6}{3a-2}$
Factor: .$\displaystyle \frac{(2a+3)(3a-2)}{3a-2}$
. . and reduce: .$\displaystyle \frac{(2a+3)({\color{red}\rlap{//////}}3a-2)}{{\color{red}\rlap{//////}}3a-2} \;=\;2a+3$
$\displaystyle \frac{5b^3+7b^2+12}{b+2}$
Factor: .$\displaystyle \frac{(b+2)(5b^2-3b+6)}{b+2}$
. . and reduce: .$\displaystyle \frac{({\color{red}\rlap{////}}b+2)(5b^2-3b+6)}{{\color{red}\rlap{////}}b+2} \;=\;5b^2-3b+6$