Question

Can someone teach me how to solve rational equations step-by-step. This is not a graded assignment.

Answer 1

To solve this question, follow the steps below.

Step 01: Factor the denominator of each fraction using (b - 3).

First,

`\begin{gathered} b^2-3b \\ b(b-3) \end{gathered}`

Second,

`\begin{gathered} b^3-3b^2 \\ b^2(b-3) \end{gathered}`

Third,

`(b-3)`

So, the expression is:

`(1)/(b(b-3))+(b^2-3b-4)/(b^2(b-3))=(1)/((b-3))`

Step 02: Write all fractions together using b²(b-3) as a denominator.

`(b*1+b^2-3b-4=b^2*1)/(b^2(b-3))`

Solve the multiplications and then the additions/subtractions in the numerator.

`\begin{gathered} (b+b^2-3b-4=b^2)/(b^2(b-3)) \\ (b^2-2b-4=b^2)/(b^2(b-3)) \end{gathered}`

Step 03: Remove the denominator.

Since both sides are divided by the same number, you can remove it.

`b^2-2b-4=b^2`

Step 04: Write all numbers on the same side of the equation.

To do it, subtract b² from both sides.

`\begin{gathered} b^2-2b-4=b^2 \\ b^2-2b-4-b^2=b^2-b^2 \\ -2b-4=0 \end{gathered}`

Step 05: Solve for b.

To do it, add 4 to both sides and then divide the sides by -2.

`\begin{gathered} -2b-4+4=0+4 \\ -2b=4 \\ (-2b)/(-2)=(4)/(-2) \\ b=-2 \end{gathered}`

Answer: b = -2.