Simplify the difference.
a^2-2a-3/a^2-9a+18 - a^2-5a-6/a^2+9a+8
(2a-3)/(a-6)
Simplify the difference.
(a^2 - 2a - 3)/(a^2 - 9a + 18) - (a^2 - 5a - 6)/(a^2 + 9a + 8)
To simplify the given expression, we first factorize the two denominators so that we can find a common denominator:
(a^2 - 9a + 18) = (a - 6)(a - 3)
(a^2 + 9a + 8) = (a + 1)(a + 8)
Now, the expression can be rewritten as:
[(a^2 - 2a - 3)/(a - 6)(a - 3)] - [(a^2 - 5a - 6)/(a + 1)(a + 8)]
The common denominator is (a - 6)(a - 3)(a + 1)(a + 8), so combining the fractions, we get:
[(a^2 - 2a - 3)(a + 1)(a + 8) - (a^2 - 5a - 6)(a - 6)(a - 3)] / [(a - 6)(a - 3)(a + 1)(a + 8)]
Expanding the numerator and then simplifying gives the final answer.
so what is the answer
The answer to the simplified expression is:
(a^2 - a - 24) / [(a - 6)(a - 3)(a + 1)(a + 8)]
simplify the complex fraction
x+4x/y/7/3x
To simplify the given complex fraction, we work through it step by step:
First, express it as a single fraction:
(x + 4x)/y / 7 / 3x
= (5x)/y / 7 / 3x
Next, convert the division by a fraction to multiplication by the reciprocal:
(5x)/y * (1/7) * (1/(3x))
= (5x)/(7y) * (1/(3x))
Now simplify by canceling common terms:
= 5 / (7y * 3)
= 5 / 21y
Therefore, the simplified form of the given complex fraction is 5 / 21y.