solve rational expressions
9 -1= 8
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x-5 x+5
To solve the rational expression, you need to find the value of x that makes the equation true.
First, you will need to clear the denominators by multiplying both sides of the equation by (x - 5)(x + 5), which is the least common denominator of the two fractions.
((9 - 1)/(x - 5)) = (8/(x + 5))
Now, you can simplify the expression by multiplying both sides of the equation by (x - 5)(x + 5):
((9 - 1)/(x - 5)) * (x - 5)(x + 5) = (8/(x + 5)) * (x - 5)(x + 5)
Simplifying further:
8(x + 5) = (9 - 1)(x - 5)
Distributing and simplifying:
8x + 40 = 8x - 8
At this point, you can see that both sides of the equation have 8x terms, and they cancel each other out. This leaves you with:
40 = -8
However, this is a contradiction, since 40 does not equal -8.
Therefore, the given rational expression has no solution.