Solve for b b/(b+1)-(b+1)/(b-4)=5/(b^2-3b-4)

Problem

b/(b+1)−(b+1)/(b−4)=5/(b2−3*b−4)

Solution

1. Factor the denominator on the right side of the equation to find the least common denominator.

b2−3*b−4=(b+1)*(b−4)

2. Identify the restricted values for b by setting the denominators to zero.

b≠−1,b≠4

3. Multiply every term in the equation by the least common denominator (b+1)*(b−4) to clear the fractions.

b*(b−4)−(b+1)*(b+1)=5

4. Expand the terms on the left side of the equation.

b2−4*b−(b2+2*b+1)=5

5. Distribute the negative sign and combine like terms.

b2−4*b−b2−2*b−1=5

−6*b−1=5

6. Isolate the variable b by adding 1 to both sides and then dividing by −6

−6*b=6

b=−1

7. Check the solution against the restricted values identified in step 2. Since b=−1 makes the original denominators zero, it is an extraneous solution.

Final Answer

b/(b+1)−(b+1)/(b−4)=5/(b2−3*b−4)⇒No solution

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