Question

simplify: x^2+2x+1/ 2x+2

Answer 1

hi :)
do you know how to factor x^2+2x+1 ?

Answer 2

2 numbers with sum = 2 , but product = 1 are ??

Answer 3

@hartnn I don't understand ? can we go through this step by step

Answer 4

thats the first step !
to factor \(ax^2 +bx+c \),
we first find 2 numbers with sum = +b and product = a*c

so for x^2+2x+1
we need to find 2 numbers with sum = +2 and product = +1
which are 2 such numbers ?

Answer 5

@hartnn x+1 is the only thing i can think of

Answer 6

how about 1 and 1
1+1 = 2
and 1*1 = 1

Answer 7

so we split 2x as x+x
\(\Large x^2+2x+1 = x^2+x+x+1\)

we can factor out x from 1st 2 terms
\(\large x (x+1)+1(x+1)\)
now we can factor out x+1
\(\large (x+1)(x+1)\)

from the denominator 2x+2, we can factor out 2
\(\large 2x+2 = 2 (x+1)\)

so we have
\(\large \dfrac{(x+1)\cancel {(x+1)}}{2\cancel{(x+1)}} = \dfrac{x+1}{2}\)
thats it!
look at the steps, and ask if you have doubts in any step.