Question

please help...

Simplify the quantity of 2 x plus 10 all over the quantity of x squared plus 4 times x minus 5.

the quantity of x plus 5 over the quantity of x minus 1
2 over the quantity of x minus 1
2 times the quantity of x plus 5 over the quantity of x minus 1
2 over x

Answer 1

\[\large \frac{2x + 10}{x^2 + 4x - 5}\]

We can simplify the bottom as

\[\large \frac{2x + 10}{(x + 5)(x - 1)}\]

If we factor out a 2 out of the top...we have

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

see anything that can cancel?

Answer 2

the x and 5??

Answer 3

Right

\[\large \frac{2\cancel{(x + 5)}}{\cancel{(x + 5)}(x - 1)}\]

which leaves us with

\[\large \frac{2}{x - 1}\]

Answer 4

so thats the answer?

Answer 5

Indeed....but do you see how I got there?

Answer 6

i dont see where you got to 5 when it was +10....

Answer 7

Okay...so just focusing on that part..

\[\large 2x + 10\]

what do each term have in common? well, they are both divisable by 2...if we divie 2x by 2...we get x....and if we divide 10 by 2...we get 5

so we can write that as

\[\large 2(x + 5)\]

Answer 8

but then wouldnt it be just x+5?

Answer 9

Not quite...because then where would that 2 have gone?

that's why we have it written outside the parenthesis...the 2 isnt gone...it's merely just "to the side" until we need it :)

Answer 10

oh ok lol thanks....

Answer 11

Because we know that if we distribute the 2 back into the parenthesis....we will get back to the 2x + 10 like we had

\[\large 2(x + 5) = 2x + 10\]

If that helps at all lol

Answer 12

oh ok