SOLUTION: solve.
3x/x^2-1=5/x
I worked it out to:
2(x-5)(x+1)
Is this correct?
Algebra.Com
Question 191061This question is from textbook saxon algebra2
: solve.
3x/x^2-1=5/x
I worked it out to:
2(x-5)(x+1)
Is this correct?
This question is from textbook saxon algebra2
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'm assuming that the equation is .
Start with the given equation
Cross multiply
Distribute and multiply
Subtract from both sides
Combine like terms.
Divide both sides by -2
Reduce
Take the square root of both sides
or Break up the "plus/minus" to form 2 separate equations.
or Simplify the square root.
So the solutions are or
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Well, I will give you high marks for creativity. But your answer isn't even close.
The two denominators have no factors in common, so the LCD is simply the product of the two, or )
. Multiplying that out would only confuse the issue, so let's leave it the way it is. Applying the LCD:
}\left(\frac{x}{x}\right) = \frac{5}{x}\left(\frac{x^2-1}{x^2-1}\right) \ \ \Rightarrow\ \ \frac{3x^2}{x(x^2 - 1)} = \frac{5(x^2-1)}{x(x^2 -1)} )
Now, use the distributive property on the numerator on the right:
} = \frac{5x^2-5}{x(x^2 -1)})
Now we have two fractions equal to each other and they have equal denominators. Therefore the numerators must be equal as well. So:
Add 
to both sides:
Multiply both sides by 
Take the square root:
But we still need to rationalize the denominator so multiply by 1 in the form of 
 \left(\frac{sqrt{2}}{sqrt{2}}\right) = \pm \frac{sqrt{10}}{2})
You should check both answers to make certain that we didn't create an extraneous root in the action of squaring the variable during the solving process.
John
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