3/x+2 + 2/x^2-4
Can somebody walk me through this, i would gladly appreciate it, ty.
Can somebody walk me through this, i would gladly appreciate it, ty.
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As with adding integer fractions such as 1/6 + 3/10, the first step is to give both fractions the same denominator.
The easiest way to do this is multiply numerator and denominator by the other fraction's denominator.
1/6 = 10/60
3/10 = 18/60
1/6 + 3/10 = (10+18)/60
3 / (x+2) = (3*(x^2 - 4)) / ((x+2) * (x^2 - 4))
But if you can find a smaller least common denominator, it will keep your numerators smaller.
Look for factors that the denominators have in common.
In this case, (x^2 - 4) is a multiple of (x+2), so the LCD is (x^2 - 4).
3 / (x+2) = 3(x - 2) / ((x+2)(x-2))
3/(x+2) + 2/(x^2 - 4) = 3(x-2)/(x^2 - 4) + 2/(x^2 - 4)
Now add the numerators.
= (3x - 6 + 2) /(x^2 - 4)
= (3x - 4) /(x^2 - 4)
If the resulting numerator shares any factors with the denominator, simplify it.
(this one doesn't)
The easiest way to do this is multiply numerator and denominator by the other fraction's denominator.
1/6 = 10/60
3/10 = 18/60
1/6 + 3/10 = (10+18)/60
3 / (x+2) = (3*(x^2 - 4)) / ((x+2) * (x^2 - 4))
But if you can find a smaller least common denominator, it will keep your numerators smaller.
Look for factors that the denominators have in common.
In this case, (x^2 - 4) is a multiple of (x+2), so the LCD is (x^2 - 4).
3 / (x+2) = 3(x - 2) / ((x+2)(x-2))
3/(x+2) + 2/(x^2 - 4) = 3(x-2)/(x^2 - 4) + 2/(x^2 - 4)
Now add the numerators.
= (3x - 6 + 2) /(x^2 - 4)
= (3x - 4) /(x^2 - 4)
If the resulting numerator shares any factors with the denominator, simplify it.
(this one doesn't)