3b-2/b+1=4-b+2/b-1
please help me I'm stuck
retype with brackets to establish the correct order of operation.
did you mean
(3b-2)/b+1 = (4-b+2)/(b-1) or
3b - 2/(b+1) = 4-b + 2/b-1 or ...
3b-2 b+2
____=4-_____
b+1 b-1
3b-2/(b+1)=4-(b+2)/b-1
still not totally clear, I will assume you mean
(3b-2)/(b+1)=4-(b+2)/(b-1)
so the LCD is (b-1)(b-1), let's multiply each term by that
(3b-2)(b-1) = 4(b-1)(b+1) - (b+2)(b+1)
for which I go
b = 4
To solve the equation 3b - 2/(b + 1) = 4 - b + 2/(b - 1), we can follow these steps:
Step 1: Simplify the expressions
Combine the like terms on both sides of the equation:
3b - 2/(b + 1) = 4 - b + 2/(b - 1)
Step 2: Get rid of the fractions
Multiply every term in the equation by the least common denominator (LCD) of (b + 1) and (b - 1) to eliminate the fractions:
(LCD) * (3b - 2/(b + 1)) = (LCD) * (4 - b + 2/(b - 1))
The LCD of (b + 1) and (b - 1) is (b + 1) * (b - 1) = (b^2 - 1).
So, the equation becomes:
(b^2 - 1) * (3b - 2/(b + 1)) = (b^2 - 1) * (4 - b + 2/(b - 1))
Step 3: Simplify and distribute
Apply the distributive property to both sides of the equation and simplify if necessary:
(3b)(b^2 - 1) - (2/(b + 1))(b^2 - 1) = (4)(b^2 - 1) - (b)(b^2 - 1) + (2/(b - 1))(b^2 - 1)
Step 4: Continue simplifying
Multiply each term by the coefficients and simplify if necessary:
3b^3 - 3b - 2(b^2 - 1)/(b + 1) = 4b^2 - 4 - b^3 + b + 2(b^2 - 1)/(b - 1)
Step 5: Get rid of the fractions
To eliminate the fractions, multiply every term by (b + 1)(b - 1) which is the denominator of the fractions:
((b + 1)(b - 1))(3b^3 - 3b) - 2(b^2 - 1) = ((b + 1)(b - 1))(4b^2 - 4 - b^3 + b) + 2(b^2 - 1)
Step 6: Simplify and distribute
Apply the distributive property and simplify if necessary:
(3b^3 - 3b)(b^2 - 1) - 2(b^2 - 1) = (4b^2 - 4 - b^3 + b)(b + 1)(b - 1) + 2(b^2 - 1)
Step 7: Combine like terms
Expand and combine like terms on both sides of the equation:
3b^5 - 3b^3 - 3b^3 + 3b - 2b^2 + 2 = 4b^4 - 4b^2 - b^4 + b^2 + 4b^3 - 4b - b^2 + b + 2b^2 - 2
Step 8: Simplify further
Combine like terms again:
3b^5 - 6b^3 + 5b - 2b^2 + 2 = 3b^4 + 3b^3 - 4b - 1
Step 9: Move all terms to one side
Move all the terms to one side so that the equation is in the form of a polynomial equal to zero:
3b^5 - 6b^3 + 5b - 2b^2 + 2 - 3b^4 - 3b^3 + 4b + 1 = 0
Step 10: Simplify and combine like terms
Combine like terms again:
3b^5 - 3b^4 - 9b^3 - 2b^2 + 9b + 3 = 0
This is now a polynomial equation of degree 5. You can proceed to solve it further using various methods such as factoring, synthetic division, or numerical approximation methods.