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Which of the following expressions is this one equivalent to?


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

Ax^3-2x+5+(7/x+5)
B3x-17+(88/x+5)
C3x^2+17-(82/x+5)
D3x^2-5x-8-(37/x+5)

...?

Verified Answer :

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,

\(3x^2+17-\frac{82}{x+5}\) is the equivalent fraction to the given expression \(\frac{3x^3+15x^2+17x+3}{x+5}\)

Step-by-step explanation:

Given expression ,  \(\frac{3x^3+15x^2+17x+3}{x+5}\)

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

Consider expression (c) ,

\(3x^2+17-\frac{82}{x+5}\)

Taking LCM , Multiply \(3x^2+17\) by (x+5) , we get,

\(\frac{3x^2(x+5)+17(x+5)-82}{x+5}\)

On solving , we get,

\(\frac{3x^3+15x^2+17x+85-82}{x+5}\)

On simplifying, we get,

\(\frac{3x^3+15x^2+17x+3}{x+5}\)

Which is equal to the given expression.

Thus, option (c) is correct,

\(3x^2+17-\frac{82}{x+5}\) is the equivalent fraction to the given expression \(\frac{3x^3+15x^2+17x+3}{x+5}\)