Please solve using the LCM as 2, x+1 and x+2?

Question

2/x+1 + 3/x+2 = 7/2

Answer 1

LCM of 2, x+1, x+2 is the product of the terms. Express everything fractions with the LCM as the denominator. Then solve.

4(x+2) / 2(x+1)(x+2) + 6(x+1) / 2(x+1)(x+2) = 7(x+1)(x+2) / 2(x+1)(x+2)

Then multiply everything by the denominator (LCM):
4(x+2) + 6(x+1) = 7(x+1)(x + 2)

Multiply out:
4x + 8 + 6x + 6 = 7(x+1)(x+2)
10x + 14 = 7(x+1)(x+2)
10x + 14 = 7(x² + 3x + 2)
10x + 14 = 7x² + 21x + 14
Put it all on one side:
7x² + 11x = 0
x(7x + 11) = 0

x = 0
or
7x + 11 = 0
7x = -11
x = -11/7

So x = 0 or x = -11/7

Answer 2

multiplying eachterm by the LCM given
4(x+2)+6(x+1)=7(x+1)(x+2)
4x+8+6x+6=7(x^2+3x+2)
10x+14=7x^2+21x+14
adding -14-10x
0=7x^2+11x
x(7x+11)=0
x=0 or -11/7

Answer 3

2/x+1 + 3/x+2 -7/2 =0
2*2*(x+2) + 3*2*(x+1) - 7(x+1)(x+2)=0
4x+8 + 6x+6 - 7x^2 -14-21x=0
-7x^2-11x=0
x=0 or -11/7

Answer 4

multiply both sides by X to get rid of X in denominator
that gives
2 + X+ 3 +2X = 7X / 2
now multiply by 2 to get rid of 2 in denominator
4+2 x + 6 +4x = 7x
4 + 6 = 7x -4x - 2x
10 = x