You can put this solution on YOUR website! 3/(x-4)+5/(x+4)=7x/(x^2-16)
[3(x+4)+5(x-4)]/(x+4)(x-4)=7/(x+4)(x-4)
[3x+12+5x-20]/(x+4)(x-4)=7/(x+4)(x-4)
(8x-8)/(x+4)(x-4)=7/(x+4)(x-4)
(8x-8-7)/(x+4)(x-4)=0
(8x-15)/(x+4)(x-4)=0 ans.
You can put this solution on YOUR website! Step 1: Simplify each side of equation
3(x+4)/(x-4)(x+4) + 5(x-4)/ (x+4)(x-4) = 7x/ (x^2 -16)
3(x+4)+ 5(x-4)/ (x+4)(x-4) = 7x/(x^2-16)
3(x+4)+5(x-4)/ (x^2-4x+4x-16)=7x/ (x^2 -16)
3(x+4)+5(x-4)/ (x^2-16) = 7x/ (x^2-16)
Now lets get rid of denominators on the left of the equation....
(x^2-16)(3(x+4)+5(x-4)/(x^2-16))=(x^2-16)(7x/(x^2-16))
3(x+4) + 5(x-4) = 7x
3x+12 +5x -20 = 7x
8x -8 =7x
x-8=0
x=8
check answer:
3 /(x-4) + 5 / (x+4) = 7x / (x^2 -16)
3/(8-4) +5/ (8+4)= 3/4 + 5/12 = 9/12 + 5/12= 14/12
7(8)/(8^2-16)= 56/(64-16)=56/48=14/12
answer is right
In order to add the two fractions on the left, you need a common denominator. Since neither of the two denominators have any common factor, the lowest common denominator is simply the product of the two denominators. Conveniently, the product of these two denominators is equal to the denominator on the right side of the equation which will make solving this much easier than otherwise.
Note that the two denominators on the left are a conjugate pair of binomials meaning that their product is the difference of two squares:
(Use FOIL to verify if you are in doubt about this). This also tells us that the values 4 and -4 must be excluded from any potential solutions to this equation because those values would cause denominators to be equal to zero making the original equation undefined.
Applying the LCD to the equation we get:
Now we can multiply both sides by the common denominator.
Collect terms:
Add to both sides:
First thing to check is that the potential solution is not contained in the set of excluded values, and we can see that so we pass the first test.
Next thing is to substitute the solution for x in the original equation and verify that it reduces to a verifiably true statement.
, which is clearly a true statement. Solution verified.
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