Simplify the expression (x^3+2x^2-7x+4)/(2x^2) | SnapXam

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 Exercise

$\frac{\left(x^3+2x^2-7x+4\right)}{2x^2}$

 Step-by-step Solution

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1

Expand the fraction $\frac{x^3+2x^2-7x+4}{2x^2}$ into $4$ simpler fractions with common denominator $2x^2$

$\frac{x^3}{2x^2}+\frac{2x^2}{2x^2}+\frac{-7x}{2x^2}+\frac{4}{2x^2}$

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2

Simplify the fraction $\frac{2x^2}{2x^2}$ by $2x^2$

$\frac{x^3}{2x^2}+1+\frac{-7x}{2x^2}+\frac{4}{2x^2}$

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3

Simplify the fraction by $x$

$\frac{x^3}{2x^2}+1+\frac{-7}{2x}+\frac{4}{2x^2}$

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4

Simplify the fraction $\frac{x^3}{2x^2}$ by $x$

$\frac{x}{2}+1+\frac{-7}{2x}+\frac{4}{2x^2}$

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5

Cancel the fraction's common factor $2$

$\frac{x}{2}+1+\frac{-7}{2x}+\frac{2}{x^2}$

Final answer to the exercise  

$\frac{x}{2}+1+\frac{-7}{2x}+\frac{2}{x^2}$

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 Main Topic: Simplification of algebraic fractions

Simplification or reduction of algebraic fractions is the action of dividing the numerator and denominator of a fraction by a common factor in order to obtain another much simpler equivalent fraction. We can say that a fraction is reduced to its simplest when there is no common factor between the numerator and the denominator.

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