Question

8. 10a - [4{5a - 3(a - 1)} - 3 (4a - 3a + 1)]

Answer 1

1). The expression to be substracted is,

`(3a)/(a^2-9)-(4a+1)/(a-3)`

Step 1: Common denominator

`(3a)/((a+3)(a-3))-((4a+1)(a+3))/((a-3)(a+3))`

Step 2: Distribute

`\begin{gathered} (3a)/((a+3)(a-3))-(4a^2+12a+a+3)/((a+3)(a-3)) \\ =(3a)/((a+3)(a-3))-(4a^2+13a+3)/((a+3)(a-3)) \end{gathered}`

Step 3: Substract

`\begin{gathered} (3a-(4a^2+13a+3))/((a+3)(a-3))=(3a-4a^2-13a-3)/((a+3)(a-3)) \\ =(-4a^2-10a-3)/((a+3)(a-3)) \end{gathered}`

Clearly there is a mistake in step 3 as negative was not multiplies to each term to be substracted.

STEP 4: Expected value

The expected value should be

`(-4a^2-10a-3)/((a+3)(a-3))`

Clearly there was a mistake in this step also due to mistake in the previous step.

Thus, there are mistakes in STEP 3 and STEP 4.