Answer:
The result becomes:
[tex]x-4+\frac{3}{x-3}[/tex]
Step-by-step explanation:
The given expression in correct order is :
[tex]\frac{x^{2}-7x+15 }{x-3}[/tex]
Now, dividing the leading coefficients of the numerator and divisor we get
[tex]\frac{x^{2} }{x}=x[/tex]
So, quotient is x
Multiplying [tex]x-3[/tex] by x
=>[tex]x^{2} -3x[/tex]
Subtracting [tex]x^{2} -3x[/tex] from [tex]x^{2} -7x+15[/tex] we get [tex]-4x+15[/tex]
This is the new remainder.
Now, the given equation becomes: [tex]x+\frac{-4x+15}{x-3}[/tex]
Dividing the leading coefficients we get [tex]\frac{-4x}{x}=-4[/tex]
Multiplying [tex]x-3[/tex] bu -4 to get [tex]-4x+12[/tex]
Subtracting [tex]-4x+12[/tex] from [tex]-4x+15[/tex] = 3
This 3 is the new remainder.
Now, the equation becomes: [tex]-4+\frac{3}{x-3}[/tex]
Therefore, the result becomes:
[tex]x-4+\frac{3}{x-3}[/tex]
