How do i solve for x in this question?

Question

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

Answer 1

If you multiply the whole equation by (x+1) to get rid of the (x+1) on the bottom of the first fraction, then multiply by (x+2) to get rid of the (x+2) on the bottom of the second fraction, then you are left with:

2(x+2) + 3(x+1) = 2(x+1)(x+2).

You can then multiply out the brackets and simplify to get in the form ax^2 + bx + c = 0, and solve like a normal quadratic equation.



Sorry suppeeps:), but you can't add the tops and bottoms of the fractions like that , thats like saying 1/2 + 1/2 = 2/4 which clearly isn't the case. You can multiply the tops and bottoms of fractions, but in order to add, they have to have the same denominator.

Answer 2

Multiply both sides of the equation by (x+1)(x+2):
2(x+2)+3(x+1)=2(x+1)(x+2)
2x+4+3x+3=2(xx+3x+2) Now simplify
2xx+x-3=0
=(2x+3)(x-1) So the roots are x= -3/2, x = 1

Answer 3

2/(x+1) + 3/(x+2) = 2

Taking LCD

2(x+2) + 3(x+1) / (x+1)(x+2) = 2

2x + 4 + 3x + 3 = 2(x+1)(x+2) (Cross multiplying)

5x + 7 = 2(x²+3x+2)
5x+7 = 2x²+6x+4
2x² + x - 3 = 0

Sum and Product of the roots
x² + x/2 - 3/2 = 0
Sum = -b/a = - (1/2 /1) = -1/2
Product = ac = -3/2

Roots = (-b ± (√b²-4ac))/2a where a , b and c are coefficients of the binomial expression , ie: a = 2 b = 1c = -3

(-(1 ) ± √(1)² - 4(2)(-3) )/ 2(2)
= (-1 ± (√1+24))/4
= (-1 ± √25)/4
= (-1 ± 5)/4
= (-1+5)/4 and
(-1 - 5)/4
= 4/4 and -6/4
The roots are 1 and -3/2

Sum of the roots = -1/2
Products of the root = -3/2.

Answer 4

2/x + 1 + 3/x + 2 = 2
5/x + 3 = 2
5/x = -1
-x = 5
x = -5

Answer 5

2/x+1+3/x+2=2
combine like terms to get:
5/x+3=2
5/x=2-3
=-1
1/x=-1/5
x=-5

Answer 6

Let 1/x=t

2t+1+3t+2=2
5t=-1
t=-1/5

x=-5

if
2/(x+1) + 3/(x+2) = 2 then
(2x+4+3x+3)/ ((x+1)(x+2))=2
=(5x+7)/((x+1)(x+2))=2
perform cross multiplication to continue

Answer 7

use x+1 and x+2 as your lcd

2(x+2) +3(x+1)= 2(x+1)(x+2)

2x+4+3x+3=2(x+1)(x+2)
5x+7=2(x^2+3x+2)
5x+7=2x^2+6x+4
2x^2+x-3 / (x+2)(x+1)
(2x+3)(x-1)
x=3/2 or 1

Answer 8

5/x+3=2
5/x=2-3
5/x=-1
5=-x
-5=x

Answer 9

[02]
2/(x+1) +3/(x+2)=2
Multiplying both sides by (x+1)(x+2)
2(x+2)+3(x+1)=2(x+1)(x+2)
2x+4+3x+3=2(x^2+3x+2)
5x+7=2x^2+6x+4
2x^2+6x+4-5x-7=0
2x^2+x-3=0
2x^2-2x+3x-3=0
2x(x-1)+3(x-1)=0
(x-1)(2x+3)=0
x=1 or -3/2