# Express ` (7x+3)/(x-1)` in the form `A + B/(x-1)` , where A and B are constants. Thanks!

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### 1 Answer

To express the given rational expression in the form A + B/(x-1), divide the numerator by the denominator using long division.

` x - 1 | bar(7x+3) `

The steps are:

> Divide 7x by x. `(7x)/x=7`

Write the 7 at the top of 7x.

> Then, multiply the resulting value by x-1. `7(x-1)=7x-7`

Write this below 7x + 3.

> Next, subtract this from 7x+3. `7x+3-(7x-7)=11`

Since 11 has no x, this is the remainder.

> And, express the remainder as a fraction and add it to 7.

`7 `

`x - 1 | bar(7x+3) `

`(-)` `7x - 7`

`-----`

`11`

**Hence, `(7x+3)/(x-1) = 7 + 11/(x-1)` .**