Question 79700: To solve 1/x-3+ 1/x+3 = 10/x^2-9, which step would result?
I got: (x+3)+(x+3) = 10
Is this correct?
Thanks~ Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! Given:
.
.
Don't think you are correct, but let's check your answer. You got:
.
.
Remove the parentheses and this becomes:
.
.
Add like terms on the left side and you get:
.
.
Subtract 6 from both sides and you get:
.
.
Then divide both sides by 2 and you finally have . If you return to the
original equation and substitute 2 for x it becomes:
.
.
Doing the math in the 3 denominators results in:
.
.
and this further simplifies to:
.
.
which becomes:
.
.
by adding +1 to both sides this becomes:
.
.
That doesn't look too good.
.
Let's go back to the original problem and work it out:
.
.
You probably recognized that the denominator on the right side factors to:
.
.
Substitute that into the equation and it becomes:
.
.
Now multiply all the terms on both sides by . When you do it becomes:
.
.
cross out the common terms in the denominator and the numerator:
.
.
and the equation becomes:
.
.
Remove the parentheses:
.
.
Combine the like terms on the left side (note +3 -3 = 0) and you get:
.
.
Finally divide both sides by 2 and you get:
.
.
Now let's check the answer. Return to the original equation and substitute 5 for x to get:
.
.
.
.
.
.
.
That works ... so the answer is x = 5
.
Hope this helps you to find your mistake.
(