Question

Tutorial ExerciseDivide.x2 + 3x – 70x2 + 2x - 63x2 + 2x – 80x2 + 6x – 16Step 1Multiply by the reciprocal of the divisor.x2 + 3x - 70x2 + 2x – 631SubmitSkip (you cannot come back)

Answer 1

First take

`(x^2+3x-70)/(x^2+2x-80)\ldots\ldots(1)`
`\begin{gathered} x^2+3x-70=x^2-7x+10x-70 \\ =x\mleft(x-7\mright)+10\mleft(x-7\mright) \\ =\mleft(x-7\mright)\mleft(x+10\mright)\ldots\text{.}\mathrm{}(2) \end{gathered}`
`\begin{gathered} x^2+2x-80=x^2-8x+10x-80 \\ =x(x-8)+10(x-8) \\ =(x-8)(x+10)\ldots\ldots\text{.}(3) \end{gathered}`

Put the values of (2) and (3) in equation (1), it becomes,

`\begin{gathered} (x^2+3x-70)/(x^2+2x-80)=((x-7)(x+10))/((x-8)(x+10)) \\ =(x-7)/(x-8)\ldots\ldots(4) \end{gathered}`
`(x^2+2x-80)/(x^2+6x-16)\ldots\text{.}(5)`

From equation (3)

`x^2+2x-80=(x-8)(x-10)`
`\begin{gathered} x^2+6x-16=x^2-2x+8x-16 \\ =x(x-2)+8(x-2) \\ =(x-2)(x+8)\ldots\ldots\text{.}\mathrm{}(6) \end{gathered}`
`(x^2+2x-80)/(x^2+6x-16)=((x-8)(x+10))/((x-2)(x+8))\ldots\text{.}(7)`

From equation (4) and (7),

`\begin{gathered} ((x^2+3x-70)/(x^2+2x-80))/((x^2+2x-80)/(x^2+6x-16))=((x-7)/(x-8))/(((x-8)(x+10))/((x-2)(x+8))) \\ =(x-7)/(x-8)\cdot((x-2)(x+8))/((x-8)(x+10)) \\ =((x-7)(x-2)(x+8))/((x-8)^2(x+10)) \end{gathered}`