I need help solving 3x-1/x+5 + 43/x^2-25= 3x+1/x-5
Your non-use of parenthesis is frustrating.
I assume you mean this:
(3x-1)/(x+5) + 43/(x^2-25)= (3x+1)/(x-5)
remember that x^2-25 is (x-5)(x+5)
now multiply both sides by
(x-5)(x+5)
sorry instead here it's
(3x-1)/(x+5) +(32)/(x^2-25)=(3x+1
)/(x-5)
yes I know that it will factor out to be (X+5)(x-5) but the thing is isn't 3x-1 only multiply by 1 since it already have (X+5) as its denominator?
To solve the given equation, let's simplify it first. The equation is:
(3x - 1)/(x + 5) + 43/(x^2 - 25) = (3x + 1)/(x - 5)
To simplify the equation, we need to find the common denominator for all the fractions involved. The common denominator for (x + 5) and (x - 5) is (x + 5)(x - 5) = x^2 - 25. Once we have the common denominator, we can multiply each term by it to eliminate the fractions.
Multiply all terms by (x^2 - 25):
(x^2 - 25) * [(3x - 1)/(x + 5)] + (x^2 - 25) * [43/(x^2 - 25)] = (x^2 - 25) * [(3x + 1)/(x - 5)]
Now simplify each term:
(3x - 1)(x^2 - 25)/(x + 5) + 43 = (3x + 1)(x^2 - 25)/(x - 5)
Expand the numerators:
(3x^3 - x^2 - 75x + 25)/(x + 5) + 43 = (3x^3 + x^2 - 75x - 25)/(x - 5)
Now combine like terms on each side of the equation:
3x^3 - x^2 - 75x + 25 + 43(x + 5) = 3x^3 + x^2 - 75x - 25(x - 5)
Simplify the equation further:
3x^3 - x^2 - 75x + 25 + 43x + 215 = 3x^3 + x^2 - 75x - 25x + 125
Combine like terms again:
3x^3 - x^2 + 68x + 240 = 3x^3 + x^2 - 100x + 125
Now subtract 3x^3 and x^2 from both sides:
68x + 240 = -100x + 125
Add 100x to both sides:
168x + 240 = 125
Subtract 240 from both sides:
168x = -115
Finally, divide by 168 to solve for x:
x = -115/168
So the solution to the equation is x = -115/168.