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Which of the following expressions is this one equivalent to?

(3x^3+15x^2+17x+3)/x+5

A. x^3-2x+5+(7/x+5)
B. 3x-17+(88/x+5)
C. 3x^2+17-(82/x+5)
D. 3x^2-5x-8-(37/x+5)

...?

Respuesta :

Nirina7
we know that 
the euclid's division A/B implies A= BQ + R
wher Q = the quotient, and R is the remainder
after doing euclid's division, (3x^3+15x^2+17x+3)/x+5 = 3x²+17and R= - 82
so (3x^3+15x^2+17x+3= (3x²+17) (x+5) -82

the answer is x^3+15x^2+17x+3= (3x²+17) (x+5) - 82

Answer:

option (c) is correct,

[tex]3x^2+17-\frac{82}{x+5}[/tex] is the equivalent fraction to the given expression [tex]\frac{3x^3+15x^2+17x+3}{x+5}[/tex]

Step-by-step explanation:

Given expression ,  [tex]\frac{3x^3+15x^2+17x+3}{x+5}[/tex]

We have to choose an equivalent fraction from the given options.

Consider expression (c) ,

[tex]3x^2+17-\frac{82}{x+5}[/tex]

Taking LCM , Multiply [tex]3x^2+17[/tex] by (x+5) , we get,

[tex]\frac{3x^2(x+5)+17(x+5)-82}{x+5}[/tex]

On solving , we get,

[tex]\frac{3x^3+15x^2+17x+85-82}{x+5}[/tex]

On simplifying, we get,

[tex]\frac{3x^3+15x^2+17x+3}{x+5}[/tex]

Which is equal to the given expression.

Thus, option (c) is correct,

[tex]3x^2+17-\frac{82}{x+5}[/tex] is the equivalent fraction to the given expression [tex]\frac{3x^3+15x^2+17x+3}{x+5}[/tex]

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