How do I solve and simplify this equation:
2 = b + b
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b-2 b^2 - 3b +2 2b-2
To solve and simplify the equation, we need to find the value of b that makes the equation true. We can do this by following these steps:
Step 1: Simplify the equation by multiplying both sides of the equation by the denominators of the fractions. This will eliminate the fractions.
2(b - 2) = (b + b)(b² - 3b + 2) - (2b - 2)
Step 2: Distribute and simplify the right side of the equation.
2(b - 2) = 2b(b² - 3b + 2) - (2b - 2)
Step 3: Simplify further.
2b - 4 = 2b³ - 6b² + 4b - (2b - 2)
Step 4: Combine like terms.
2b - 4 = 2b³ - 6b² + 4b - 2b + 2
Step 5: Simplify the equation.
2b - 4 = 2b³ - 6b² + 2
Step 6: Move all terms to one side of the equation, so that the equation is equal to zero.
2b³ - 6b² + 2 - 2b + 4 = 0
Step 7: Combine like terms.
2b³ - 6b² - 2b + 6 = 0
Now, to solve this equation, we can either factor it or use numerical methods like graphing or using a calculator. Factoring this equation might not be straightforward, so let's use numerical methods.