Simplify limit as x approaches negative infinity of x/(2x-3)

Solve Math

Algebra

$lim_{x \to - \infty} \frac{x}{2 x - 3}$

Divide the numerator and denominator by the highest power of $x$ in the denominator, which is $x$ .

$lim_{x \to - \infty} \frac{\frac{x}{x}}{\frac{2 x}{x} + \frac{- 3}{x}}$

Evaluate the limit.

Tap for more steps...

Cancel the common factor of $x$ .

Tap for more steps...

Cancel the common factor.

$lim_{x \to - \infty} \frac{\frac{x}{x}}{\frac{2 x}{x} + \frac{- 3}{x}}$

Rewrite the expression.

$lim_{x \to - \infty} \frac{1}{\frac{2 x}{x} + \frac{- 3}{x}}$

Simplify each term.

Tap for more steps...

Cancel the common factor of $x$ .

Tap for more steps...

Cancel the common factor.

$lim_{x \to - \infty} \frac{1}{\frac{2 x}{x} + \frac{- 3}{x}}$

Divide $2$ by $1$ .

$lim_{x \to - \infty} \frac{1}{2 + \frac{- 3}{x}}$

Move the negative in front of the fraction.

$lim_{x \to - \infty} \frac{1}{2 - \frac{3}{x}}$

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $- \infty$ .

$\frac{lim_{x \to - \infty} 1}{lim_{x \to - \infty} 2 - \frac{3}{x}}$

Evaluate the limit of $1$ which is constant as $x$ approaches $- \infty$ .

$\frac{1}{lim_{x \to - \infty} 2 - \frac{3}{x}}$

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $- \infty$ .

$\frac{1}{lim_{x \to - \infty} 2 - lim_{x \to - \infty} \frac{3}{x}}$

Evaluate the limit of $2$ which is constant as $x$ approaches $- \infty$ .

$\frac{1}{2 - lim_{x \to - \infty} \frac{3}{x}}$

Move the term $3$ outside of the limit because it is constant with respect to $x$ .

$\frac{1}{2 - 3 lim_{x \to - \infty} \frac{1}{x}}$

Since its numerator approaches a real number while its denominator is unbounded, the fraction $\frac{1}{x}$ approaches $0$ .

$\frac{1}{2 - 3 \cdot 0}$

Simplify the denominator.

Tap for more steps...

Multiply $- 3$ by $0$ .

$\frac{1}{2 + 0}$

Add $2$ and $0$ .

$\frac{1}{2}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$

Do you know how to Simplify limit as x approaches negative infinity of x/(2x-3)? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Evaluate log of 2

Evaluate log base 9 of 27

Simplify (-2-i)(4+i)

Solve by Completing the Square x^2+22x=31

Convert to Radical Form y^(-8/7)