Simplify (1-4/x+3/(x^2))/(1+1/x-12/(x^2))

$\frac{1 - \frac{4}{x} + \frac{3}{x^{2}}}{1 + \frac{1}{x} - \frac{12}{x^{2}}}$

Multiply the numerator and denominator of the complex fraction by $x^{2}$ .

Multiply $\frac{1 - \frac{4}{x} + \frac{3}{x^{2}}}{1 + \frac{1}{x} - \frac{12}{x^{2}}}$ by $\frac{x^{2}}{x^{2}}$ .

$\frac{x^{2}}{x^{2}} \cdot \frac{1 - \frac{4}{x} + \frac{3}{x^{2}}}{1 + \frac{1}{x} - \frac{12}{x^{2}}}$

Combine.

$\frac{x^{2} (1 - \frac{4}{x} + \frac{3}{x^{2}})}{x^{2} (1 + \frac{1}{x} - \frac{12}{x^{2}})}$

Apply the distributive property.

$\frac{x^{2} \cdot 1 + x^{2} (- \frac{4}{x}) + x^{2} \frac{3}{x^{2}}}{x^{2} \cdot 1 + x^{2} \frac{1}{x} + x^{2} (- \frac{12}{x^{2}})}$

Simplify by cancelling.

Cancel the common factor of $x$ .

Move the leading negative in $- \frac{4}{x}$ into the numerator.

$\frac{x^{2} \cdot 1 + x^{2} \frac{- 4}{x} + x^{2} \frac{3}{x^{2}}}{x^{2} \cdot 1 + x^{2} \frac{1}{x} + x^{2} (- \frac{12}{x^{2}})}$

Factor $x$ out of $x^{2}$ .

$\frac{x^{2} \cdot 1 + x \cdot x \frac{- 4}{x} + x^{2} \frac{3}{x^{2}}}{x^{2} \cdot 1 + x^{2} \frac{1}{x} + x^{2} (- \frac{12}{x^{2}})}$

Cancel the common factor.

$\frac{x^{2} \cdot 1 + x \cdot x \frac{- 4}{x} + x^{2} \frac{3}{x^{2}}}{x^{2} \cdot 1 + x^{2} \frac{1}{x} + x^{2} (- \frac{12}{x^{2}})}$

Rewrite the expression.

$\frac{x^{2} \cdot 1 + x \cdot - 4 + x^{2} \frac{3}{x^{2}}}{x^{2} \cdot 1 + x^{2} \frac{1}{x} + x^{2} (- \frac{12}{x^{2}})}$

Cancel the common factor of $x^{2}$ .

Cancel the common factor.

$\frac{x^{2} \cdot 1 + x \cdot - 4 + x^{2} \frac{3}{x^{2}}}{x^{2} \cdot 1 + x^{2} \frac{1}{x} + x^{2} (- \frac{12}{x^{2}})}$

Rewrite the expression.

$\frac{x^{2} \cdot 1 + x \cdot - 4 + 3}{x^{2} \cdot 1 + x^{2} \frac{1}{x} + x^{2} (- \frac{12}{x^{2}})}$

Cancel the common factor of $x$ .

Factor $x$ out of $x^{2}$ .

$\frac{x^{2} \cdot 1 + x \cdot - 4 + 3}{x^{2} \cdot 1 + x \cdot x \frac{1}{x} + x^{2} (- \frac{12}{x^{2}})}$

Cancel the common factor.

$\frac{x^{2} \cdot 1 + x \cdot - 4 + 3}{x^{2} \cdot 1 + x \cdot x \frac{1}{x} + x^{2} (- \frac{12}{x^{2}})}$

Rewrite the expression.

$\frac{x^{2} \cdot 1 + x \cdot - 4 + 3}{x^{2} \cdot 1 + x + x^{2} (- \frac{12}{x^{2}})}$

Cancel the common factor of $x^{2}$ .

Move the leading negative in $- \frac{12}{x^{2}}$ into the numerator.

$\frac{x^{2} \cdot 1 + x \cdot - 4 + 3}{x^{2} \cdot 1 + x + x^{2} \frac{- 12}{x^{2}}}$

Cancel the common factor.

$\frac{x^{2} \cdot 1 + x \cdot - 4 + 3}{x^{2} \cdot 1 + x + x^{2} \frac{- 12}{x^{2}}}$

Rewrite the expression.

$\frac{x^{2} \cdot 1 + x \cdot - 4 + 3}{x^{2} \cdot 1 + x - 12}$

Factor $x^{2} \cdot 1 + x \cdot - 4 + 3$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $3$ and whose sum is $- 4$ .

$- 3, - 1$

Write the factored form using these integers.

$\frac{(x - 3) (x - 1)}{x^{2} \cdot 1 + x - 12}$

Factor $x^{2} \cdot 1 + x - 12$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 12$ and whose sum is $1$ .

$- 3, 4$

Write the factored form using these integers.

$\frac{(x - 3) (x - 1)}{(x - 3) (x + 4)}$

Cancel the common factor of $x - 3$ .

Cancel the common factor.

$\frac{(x - 3) (x - 1)}{(x - 3) (x + 4)}$

Rewrite the expression.

$\frac{x - 1}{x + 4}$

Simplify (1-4/x+3/(x^2))/(1+1/x-12/(x^2))

Related Questions

Support LCMGCF.com by disabling your adblocker.