2x+5 x+4
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x^2+3x+2 x^2+3x+2
i keep getting
x+9
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(x+1)(x+2)
We can't tell by reading
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7x + 4
(2x+5)/(x^2+3x+2) - (x+4)/(x^2+3x+2)
= (2x+5-x-4)/(x^2+3x+2)
= (x+1) / (x+1)(x+2)
= 1/(x+2)
To simplify the expression, we need to combine the two fractions and find a common denominator.
The first step is to factorize the denominators of both fractions: x^2 + 3x + 2.
The factors of the quadratic x^2 + 3x + 2 are (x + 1) and (x + 2). Therefore, the common denominator for both fractions is (x + 1)(x + 2).
Now, let's rewrite both fractions with the common denominator:
(2x + 5)/(x^2 + 3x + 2) - (x + 4)/(x^2 + 3x + 2)
Now, since both fractions have the same denominator, we can combine them by subtracting the numerators while keeping the denominator the same:
(2x + 5 - (x + 4))/(x^2 + 3x + 2)
Simplifying the numerator:
(2x + 5 - x - 4)/(x^2 + 3x + 2)
Combining like terms:
(x + 1)/(x^2 + 3x + 2)
Factoring the quadratic in the denominator:
(x + 1)/[(x + 1)(x + 2)]
Simplifying the expression, we can cancel out the common factor of x + 1:
1/(x + 2)
Therefore, the simplified expression is:
1/(x + 2) or simply 1/(x + 2)