Question

Which of the following rational algebraic expression is written in simplest form?

- x2+2x-3/x+3
- 4abc/16
- x2-x-2/x-1
- 15mn/35mn​

Answer 1

x^2 + 2x - 3 / x + 3 = x - 1

4abc / 16 = abc / 4

x2 - x - 2 / x - 1 = ( x + 1 ) ( x - 2 ) / ( x - 1 )

15mn / 35mn = 3 / 7

Explanation:

x^2 + 2x - 3

= x^2 - x + 3x - 3

= x ( x - 1 ) + 3 ( x - 1 )

= ( x + 3 ) ( x - 1 )

x^2 + 2x - 3 / x + 3

= ( x + 3 ) ( x - 1 ) / ( x + 3 )

= x - 1

4abc / 16

= 4 * abc / 4 * 4

= abc / 4

x^2 - x - 2

= x^2 + x - 2x - 2

= x ( x + 1 ) - 2 ( x + 1 )

= ( x + 1 ) ( x - 2 )

x^2 - x - 2 / x - 1

= ( x + 1 ) ( x - 2 ) / ( x - 1 )

15mn / 35mn

= 3 x 5 x mn / 5 x 7 x mn

= 3 / 7