2/x + (x+2)/(x+1) = 7/2?

Question

Solve by factoring.
Can someone please explain this to me step by step.
Thank you! I'm studying for my NYS Math Regents!

It reads: Two over x plus x plus two over x plus one is equal to seven over two.

Answer 1

Multiply all by the LCM: 2x(x+1)

4(x+1) + 2x(x+2)=7x(x+1)

4x+4+2x2+4x=7x+7
2x2+x-3=0
2(x+3/2)(x-1)=0

x=-3/2
x=1

Answer 2

Multiply both sides by 2(x)(x+1) , getting:
4(x+1) + 2x(x+1) = 7 x(x+1)
4x+4 +2x^2 +2x = 7x^2 +7x
5x^2 + x -4 = 0
(5x-4)(x+1) = 0
x = 4/5 or -1

Answer 3

you multiply by (x+1)x
2(x+1) + (x+2)x = 7/2
2x+2+x^2+2x = 7/2
x^2 + 4x + 2 - 7/2 = 0
x^2 + 4x -3/2 = 0

multiply by 2 to get integer number et the end:
2x^2 + 8x -3 = 0

then use quadratic formula or complete the square (you can't factor).

Answer 4

2/x + (x+2)/(x+1) = 7/2

Using fractions

[2(x+1)+x(x+2)]/x(x+1)=7/2

=2x+2+x^2+2x/x(x+1)=7/2

=x^2+4x+2/x(x+1)=7/2

=2(x^2+4x+2)=7x(x+1)
=2x^2+8x+4=7x^2+7x
=> 5x^2-x-4=0

Factorising the above:

(5x+4)(x-1)=0

x=1 and x=-4/5