(3b-2)/(b+1) = (4)- (b+2)/(b-1)
The (b+2)/(b-1) is separate from the 4. the 4 isn't included in the division
multipy both sides by (b+1)(b-1)
(3b-2)(b-1)= 4(b^2-1) - (b+2)(b+1)
now foil each term out, then combine terms, and factor (or use the quadratic equation).
does b=2???
To solve the equation (3b-2)/(b+1) = 4 - (b+2)/(b-1), we need to remove the fractions and simplify the equation.
Step 1: Remove the fractions by multiplying both sides of the equation by the least common denominator (LCD) of the fractions involved. In this case, the LCD is (b+1)(b-1).
After multiplying, we get:
(b+1)(b-1) * [(3b-2)/(b+1)] = (b+1)(b-1) * [4 - (b+2)/(b-1)]
Expanding both sides gives:
(3b-2)(b-1) = 4(b+1)(b-1) - (b+2)(b+1)
Now, let's simplify each side of the equation separately.
On the left side:
(3b-2)(b-1) can be expanded using the distributive property:
3b(b-1) - 2(b-1) = 3b^2 - 3b - 2b + 2
Simplifying further gives:
3b^2 - 5b + 2
On the right side:
4(b+1)(b-1) - (b+2)((b+1))
Expand each term using the distributive property:
4(b^2 - 1) - (b^2 + 3b + 2)
Simplifying further gives:
4b^2 - 4 - b^2 - 3b - 2
Combining like terms:
(4b^2 - b^2) + (-3b) + (4 - 4 - 2) = 3b^2 - 3b - 2
Now our equation becomes:
3b^2 - 5b + 2 = 3b^2 - 3b - 2
Step 2: Subtract 3b^2 from both sides of the equation to isolate the variable terms:
(-5b + 2) = (-3b - 2)
Step 3: Add 5b to both sides to simplify the equation further:
5b - 5b + 2 = -3b + 5b - 2
2 = 2b - 2
Step 4: Add 2 to both sides of the equation:
2 + 2 = 2b - 2 + 2
4 = 2b
Step 5: Finally, divide both sides by 2 to solve for b:
4/2 = 2b/2
2 = b
Therefore, the solution to the equation (3b-2)/(b+1) = 4 - (b+2)/(b-1) is b = 2.