SOLUTION: (1/x+1) + (1/x+2) = 1
This question was on my homework, but our teacher hasn't taught it to us yet. Please can you help? Thank you?
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Question 1031682: (1/x+1) + (1/x+2) = 1
This question was on my homework, but our teacher hasn't taught it to us yet. Please can you help? Thank you?
Found 4 solutions by Fombitz, fractalier, ikleyn, rothauserc:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Just like with fractions, use a common denominator,
Equate the numerators,
Complete the square,
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
What you do with
is multiply everything by the lowest common denominator, (x+1)(x+2)...we get
Now solve for x...we get
which cannot be factored...you'll have to apply the quadratic formula from here...
Answer by ikleyn(52847) (Show Source): You can put this solution on YOUR website!
.
Shortly speaking, multiply both sides by (x+1)*(x+2) to rid off the denominators,
and then solve the obtained quadratic equation.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
(1/(x+1)) + (1/(x+2)) = 1
:
the common denominator is (x+1)*(x+2)
:
multiply both sides of the = by the common denominator
:
(x+2) + (x+1) = x^2+3x+2
:
x^2 +x -1 = 0
:
x^2 +x = 1
:
complete the square
:
x^2 +x + (1/4) = 1 + (1/4)
:
(x+(1/2))^2 = 5/4
:
take square root of both sides
x+(1/2) = square root(5)/2
:
**************************************************
x = square root(5)/2 - (1/2) = 0.618033989
x = -square root(5)/2 - (1/2) = −1.618033989
**************************************************
:
check the work by substituting for x in given equation
:
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