Divide the numerator and denominator by the highest power of <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> in the denominator, which is <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Simplify each term.

Cancel the common factor of <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Move the negative in front of the fraction.

Split the limit using the Limits Quotient Rule on the limit as <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> approaches <math><mstyle displaystyle="true"><mo>-</mo><mi>∞</mi></mstyle></math> .

Evaluate the limit of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> which is constant as <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> approaches <math><mstyle displaystyle="true"><mo>-</mo><mi>∞</mi></mstyle></math> .

Split the limit using the Sum of Limits Rule on the limit as <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> approaches <math><mstyle displaystyle="true"><mo>-</mo><mi>∞</mi></mstyle></math> .

Evaluate the limit of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> which is constant as <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> approaches <math><mstyle displaystyle="true"><mo>-</mo><mi>∞</mi></mstyle></math> .

Move the term <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> outside of the limit because it is constant with respect to <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Since its numerator approaches a real number while its denominator is unbounded, the fraction <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mi>x</mi></mrow></mfrac></mstyle></math> approaches <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

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