Respuesta :
Answer:
The division for the provided expression is:[tex]w-2-\frac{1}{w+1}[/tex].
Step-by-step explanation:
Consider the provided polynomial expression:
[tex]\frac{w^2-w-3}{w+1}[/tex]
Apply the long division.
Divide the leading coefficients of the numerator [tex]w^2-w-3[/tex] and the divisor [tex]w+1\mathrm{\::\:}\frac{w^2}{w}=w[/tex]
Therefore the quotient is w.
Multiply [tex]w+1\mathrm{\:by\:}w:\:w^2+w[/tex]
Subtract [tex]w^2+w[/tex] from [tex]w^2-w-3[/tex] to get new remainder.
Thus, the remainder is [tex]-2w-3[/tex]
Therefore,
[tex]\frac{w^2-w-3}{w+1}=w+\frac{-2w-3}{w+1}[/tex]......(1)
Divide the leading coefficient of the numerator [tex]-2w-3[/tex] and the divisor [tex]w+1\mathrm{\::\:}\frac{-2w}{w}=-2[/tex]
Thus the quotient is -2
Now, multiply [tex]w+1[/tex] by -2 which gives [tex]-2w-2[/tex].
Subtract [tex]-2w-2[/tex] from [tex]-2w-3[/tex] to get new remainder.
Thus, the remainder is -1
Therefore, [tex]\frac{-2w-3}{w+1}=-2+\frac{-1}{w+1}[/tex]
Now replace the value of [tex]\frac{-2w-3}{w+1}=-2+\frac{-1}{w+1}[/tex] in equation 1.
Thus, we get [tex]w-2-\frac{1}{w+1}[/tex].
Therfore, the division for the provided expression is [tex]w-2-\frac{1}{w+1}[/tex].
