Question

what value is a discontinuity of x^2+5x+2/x^2+2x-35

Answer 1

that's a fraction. find the values of x which cause the denominator to be 0 and you'll find the discontinuities.

Answer 2

do I just subtract

Answer 3

set x^2 + 2x - 35 = 0 and solve for x

you could factor, or use the quadratic formula, or complete the square, or graph it, or any of a number of ways

Answer 4

to factor it, you need to think of a pair of numbers that add to +2, and multiply to -35

Answer 5

7 and -5

Answer 6

right. so we can write that as
(x+7)(x-5) = 0

what are the values of x that make that expression true? those are the discontinuities of that fraction.

Answer 7

if we have a product that equals 0, that means that any or all of the terms must each equal 0.

(x+7)(x-5) = 0
(x+7) = 0
x = -7
(x-5) = 0
x = 5

so those are the discontinuities. As a quick check, let's evaluate the denominator of the fraction at those values:

x = 5
x^2 + 2x -35 = 5^2 + 2(5) -35 = 25 + 10 - 35 = 0
can't divide by 0, so that's a discontinuity

x = -7
x^2 + 2x -35 = (-7)^2 + 2(-7) - 35 = 49 -14 -35 = 0
again, can't divide by 0, so that's a discontinuity

Answer 8

I would have never gotten this without you

Answer 9

but now you know how these and can go forth with confidence! :-)

Answer 10

how to do these, that is

Answer 11

yes I have another question if you would like to help

Answer 12

I'd like to, but I have to leave, sorry!

Answer 13

its okay