Question

x+9/5x^2+6x+1 plus x/5x^2+7x+2

Answer 1

\[\frac{x+9}{5x^2+6x+1}+\frac{x}{5x^2+7x+2}\]
\[=\frac{x+9}{(x+1)(5x+1)}+\frac{x}{(x+1)(5x+2)}\]

Answer 2

ok i lied, there is a common factor. it is x+1

Answer 3

so least common denominator will be
\[(x+1)(5x+1)(5x+2)\]

Answer 4

mulitply top and bottom of first fraction by 5x+2 and second by 5x+1

Answer 5

\[\frac{(x+9)(5x+2)}{(x+1)(5x+1)(5x+2)}+\frac{x(5x+1)}{(x+1)(5x+1)(5x+2)}\]

Answer 6

=\[\frac{(x+9)(5x+2)+x(5x+1)}{(x+1)(5x+1)(5x+2)}\]

Answer 7

now mulitply out in the numerator and combine like terms you get for the numerator
\[10x^2+48x+18\]

Answer 8

so your 'final answer" is
\[\frac{10x^2+48x+18}{(x+1)(5x+1)(5x+2)}\]

Answer 9

No! x+9/5x^2+6x+1 plus x/5x^2+7x+2 means
x+(9/5x^2)+6x+1 + (x/5x^2)+7x+2

Answer 10

i doubt it

Answer 11

It's what the OP wrote. If OP meant it differently, then parens needed to be used.

Answer 12

that is why there were common factors in the denominator, so you can realize that the common denominator need not be the product of the two denominators. just take the factors

Answer 13

You can't assume that. That's what parens are meant for. lol