Are these two expressions equal? `(x^2+4x-1)/(x+1)`  `=` `(x+3)` `-` `4/(x+1)`  Grateful for an answer..

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jgeertz | College Teacher | (Level 1) Associate Educator

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Yes, these two expressions are equal.

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

 

Multiply each term so that all terms have a denominator of (x+1).

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

The numerators of expressions with equal denominators can be combined.

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

Combine similar terms in the polynomial.

`(x^2+4x-1)/(x+1)=(x^2+4x-1)/(x+1)`

Multiply each term in the equation by (x+1) to get rid of the denominators.

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

Simplify.

`x^2+4x-1=x^2+4x-1`

`x^2+4x-1-x^2-4x =-1`

Since `x^2` and `-x^2` cancel each other out and `+4x` and `-4x` also cancel, we are left with

`-1=-1`

Since `-1=-1` , the expressions are equal.

 

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