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Answer:
x=-1
Step-by-step explanation:
x+3
------- = 3 + 1/x
x+2
Get a common denominator on the right
3*x/x + 1/x
3x/x + 1/x = (3x+1)/x
x+3 3x+1
------- = ---------
x+2 x
We can use cross products to solve
(x+3) *x = (3x+1) * (x+2)
x^2+3x = 3x*x +x + 3x*2 +2
Simplifying
x^2 + 3x = 3x^2 +7x+2
Subtract x^2 from each side
x^2 -x^2 + 3x = 3x^2-x^2 +7x+2
3x = 2x^2 +7x+2
Subtract 3x from each side
3x-3x = 2x^2 +7x -3x+2
0 = 2x^2 +4x +2
Divide by 2
0 = x^2 +2x +1
Factor
0 = (x+1) (x+1)
Using the zero product property
x+1 =0
x=-1
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Rewritten by : Barada
Answer:
The solution set is { -1 }.
Step-by-step explanation:
If we multiply each term by the LCM of x and x+ 2 ( = x(x + 2)) we get:-
x(x + 3) = 3x(x + 2) + x + 2
x^2 + 3x = 3x^2 + 6x + x + 2
0 = 3x^2 - x^2 - 3x + 6x + x + 2
2x^2 +4x + 2 = 0
2(x^2 + 2x + 1) = 0
2( x + 1)(x + 1) = 0
x = -1 Multiplicity 2
The solution set only contains 1 * -1 . Elements in a set are not repeated
So its {-1} (answer)
