Simplify 2x + 10 / x^2 + 4x – 5
X + 5 / x – 1
2 / x – 1
2(x + 5) / x – 1
2 / x

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hartnn (hartnn):

can you factor x^2 + 4x – 5 ?

OpenStudy (anonymous):

forgot

hartnn (hartnn):

what are the 2 numbers with sum =4 and product = -5 ?

OpenStudy (anonymous):

4x and -5

hartnn (hartnn):

you mean 4 and -5 ?
not really...

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OpenStudy (anonymous):

ok

hartnn (hartnn):

try again ?

OpenStudy (anonymous):

2 and 10

hartnn (hartnn):

2+10 =4 ?

hartnn (hartnn):

and one of the number will be negative.

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OpenStudy (anonymous):

oh 2x and x^2 = 4

OpenStudy (anonymous):

10 - 5 = 5

hartnn (hartnn):

what about +5 and -1 ?

OpenStudy (anonymous):

4

hartnn (hartnn):

will those give sum =4 and product = -5 ?

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OpenStudy (anonymous):

yes

hartnn (hartnn):

so, we split the middle term
4x = 5x-x

OpenStudy (anonymous):

ok

hartnn (hartnn):

x^2+5x-x-5 =0
x(x+5)-1 (x+5) =0
factor out x+5 from that, what u get ?

OpenStudy (anonymous):

ok so im gonna have
(x + 5) and also -1

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hartnn (hartnn):

and there was +x in the beginning also, right ?
so , you have
(x-1)(x+5) as your denominator, ok ?
what about numerator 2x+10
factor out 2, what u get ?

OpenStudy (anonymous):

12x

hartnn (hartnn):

how ?

OpenStudy (anonymous):

well adding them both together

hartnn (hartnn):

you can't add 2x to 10
2x has 'x' in it, its variable, 10 is a constant

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OpenStudy (anonymous):

oh srry

OpenStudy (anonymous):

im not sure then

hartnn (hartnn):

2*x+10 = 2*x+2*5
2 is common, factoring it out,
2 (x+5)
got this ?

OpenStudy (anonymous):

yup

hartnn (hartnn):

numerator = 2 (x+5)
denominator = (x-1)(x+5)
what gets cancelled out ?

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OpenStudy (anonymous):

x + 5

hartnn (hartnn):

what remains ?

OpenStudy (anonymous):

2 / x - 1

hartnn (hartnn):

thats your answer :)

OpenStudy (anonymous):

thank you for all your help

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