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Answer:
[tex]\frac{(2x-3)(x+7)}{x+3}[/tex]
Step-by-step explanation:
Given
[tex]\frac{2x^3+11x^2-21x}{x^2+3x}[/tex]
Required
Select equivalent expression
[tex]\frac{2x^3+11x^2-21x}{x^2+3x}[/tex]
Factorize the numerator and denominator
[tex]\frac{x(2x^2+11x-21)}{x(x+3)}[/tex]
Divide by x/x
[tex]\frac{2x^2+11x-21}{x+3}[/tex]
Expand the numerator
[tex]\frac{2x^2+14x-3x-21}{x+3}[/tex]
Factorize the numerator
[tex]\frac{2x(x+7)-3(x+7)}{x+3}[/tex]
[tex]\frac{(2x-3)(x+7)}{x+3}[/tex]
Hence, the equivalent expression is:
[tex]\frac{(2x-3)(x+7)}{x+3}[/tex]