Question

A^2+2a+1/b^2-4*b+2/a+1-a/b+2

Answer 1

$\frac{a^{2}+2a+1 }{b^{2}-4 }*\frac{b+2}{a+1}-\frac{a}{b+2}=\frac{(a+1)^{2}}{(b+2)(b-2)}*\frac{b+2}{a+1}-\frac{a}{b+2}=\frac{a+1}{b-2}-\frac{a}{b+2}=\frac{ab+2a+b+2-ab+2a}{(b-2)(b+2)}=\frac{4a+b+2}{b^{2}-4 }$

Answer 2

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Answer 3

To simplify the given expression, let's group the terms appropriately and combine like terms:

Expression: $\frac{a^2 + 2a + 1}{b^2 - 4b + 2} + \frac{a + 1 - a}{b + 2}$

Step 1: Factorize the denominators where possible. The denominator of the first fraction can't be factorized further: $b^2 - 4b + 2$

Step 2: Find a common denominator for both fractions. The common denominator for $b^2 - 4b + 2$ and $b + 2$ is $(b^2 - 4b + 2)(b + 2)$.

Step 3: Rewrite both fractions with the common denominator. $\frac{(a^2 + 2a + 1)(b + 2)}{(b^2 - 4b + 2)(b + 2)} + \frac{(a + 1 - a)(b^2 - 4b + 2)}{(b^2 - 4b + 2)(b + 2)}$

Step 4: Simplify each fraction. The first fraction is already simplified as much as possible, as is the second fraction: $\frac{(a^2 + 2a + 1)(b + 2) + (-3b^2 + 12b - 2)}{(b^2 - 4b + 2)(b + 2)}$

Step 5: Combine the terms in the numerator. $\frac{a^2b + 2ab + b + 2a^2 + 4a - 3b^2 + 12b - 2}{(b^2 - 4b + 2)(b + 2)}$

Step 6: No further simplification can be done, so the final expression is: $\frac{a^2b + 2ab + b + 2a^2 + 4a - 3b^2 + 12b - 2}{(b^2 - 4b + 2)(b + 2)}$