Question

Simplify the given expression; Add and subtract rational expressions. (1/4x^2) + (6/2x+5)

Answer 1

you should start by unpacking the first set of terms with the exponent in it. can you factor that out using just a standard factoring method?

Answer 2

thats what i dont understand how to do.

Answer 3

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

Answer 4

to factor, 4x^2 -25.. you need to figure out what terms you can multiply the C, or constant terms by in order to end up with the middle term.. which in this case isnt there. so its 0... so it has to be something that multiplies to -25 and adds up to 0 for the middle term

Answer 5

do you understand how to foil?

Answer 6

\[4x ^{2} - 25\] is like \[4x ^{2} + 0x - 25\] to make it easier to understand

Answer 7

so now you can see the three terms.

Answer 8

so you know x(x) is x^2 and u know that 2x(2x) is 4x2.. so that can go (2x )(2x )

Answer 9

now look at the term -25.. what can u multiply to make negative 25 that also equals 0 when you add them up?

Answer 10

now that we have factored the term.. you should multiply the numerators and denominators by the least common denominator. do you understand how to do that?

Answer 11

yes i do.

Answer 12

ok you got it from here then?

Answer 13

a tip.. you can use the quadratic formula to find out the roots for factoring as well. the ti 83 graphing calc can be programmed for it.. and will save you a lot of time checking your work.