Question

2b²-b\b³+1 - b-1\b²-b+1

Answer 1

$\frac{2b^{2}-b} {b^{3}+1}- \frac{b-1}{b^{2}-b+1}= \frac{2b^{2}-b} {(b+1)(b^{2}-b+1)}- \frac{b-1}{b^{2}-b+1}= \frac{2b^{2}-b-b^{2}+1}{(b+1)(b^{2}-b+1)}= \frac{b^{2}-b+1} {(b+1)(b^{2}-b+1)}= \frac{1}{b+1}$

Answer 2

To simplify the given expression, we need to perform the indicated operations and combine like terms. The expression is:

2b² - (b/b³ + 1) - (b-1/b² - b + 1)

Step 1: Simplify the fractions inside the parentheses.

b/b³ + 1 = 1/b² + 1 = (1 + b²) / b²

b-1/b² - b + 1 = (b² - 1)/b² - (b² - b + 1) = (b² - 1 - b² + b - 1)/b² = (b - 2)/b²

So the expression becomes:

2b² - (1 + b²)/b² - (b - 2)/b²

Step 2: Find a common denominator, which is b², for all the terms.

2b² = (2b² * b²) / b² = (2b^4) / b²

(1 + b²)/b² = ((1 + b²) * b²) / b² = (b² + b^4) / b²

(b - 2)/b² = ((b - 2) * b²) / b² = (b^3 - 2b²) / b²

Now the expression is:

(2b^4) / b² - (b² + b^4) / b² - (b^3 - 2b²) / b²

Step 3: Combine the fractions using the common denominator.

(2b^4 - b² - b^4 - b^3 + 2b²) / b²

Step 4: Combine like terms in the numerator.

(2b^4 - b^4 - b^3 - b² + 2b²) / b²

Step 5: Simplify further.

(b^4 - b^3 + b²) / b²

So the simplified expression is:

b^4 - b^3 + b² / b²

And since b² / b² equals 1, the final result is:

b^4 - b^3 + b²