Solve left(a-4right)left(3-frac{6/asqrt{a}right)}{left(3-12/aright)left(a-2sqrt{a}right)}

$$\frac{ \left( a-4 \right) \left( 3- \frac{ 6 }{ a } \sqrt{ a } \right) }{ \left( 3- \frac{ 12 }{ a } \right) \left( a-2 \sqrt{ a } \right) }$$

Evaluate

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Short Solution Steps

Express \frac{6}{a}\sqrt{a} as a single fraction.

$$\frac{\left(a-4\right)\left(3-\frac{6\sqrt{a}}{a}\right)}{\left(3-\frac{12}{a}\right)\left(a-2\sqrt{a}\right)}$$

Cancel out \sqrt{a} in both numerator and denominator.

$$\frac{\left(a-4\right)\left(3-\frac{6}{\sqrt{a}}\right)}{\left(3-\frac{12}{a}\right)\left(a-2\sqrt{a}\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{\sqrt{a}}{\sqrt{a}}.

$$\frac{\left(a-4\right)\left(\frac{3\sqrt{a}}{\sqrt{a}}-\frac{6}{\sqrt{a}}\right)}{\left(3-\frac{12}{a}\right)\left(a-2\sqrt{a}\right)}$$

Since \frac{3\sqrt{a}}{\sqrt{a}} and \frac{6}{\sqrt{a}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(a-4\right)\times \frac{3\sqrt{a}-6}{\sqrt{a}}}{\left(3-\frac{12}{a}\right)\left(a-2\sqrt{a}\right)}$$

Express \left(a-4\right)\times \frac{3\sqrt{a}-6}{\sqrt{a}} as a single fraction.

$$\frac{\frac{\left(a-4\right)\left(3\sqrt{a}-6\right)}{\sqrt{a}}}{\left(3-\frac{12}{a}\right)\left(a-2\sqrt{a}\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{a}{a}.

$$\frac{\frac{\left(a-4\right)\left(3\sqrt{a}-6\right)}{\sqrt{a}}}{\left(\frac{3a}{a}-\frac{12}{a}\right)\left(a-2\sqrt{a}\right)}$$

Since \frac{3a}{a} and \frac{12}{a} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\left(a-4\right)\left(3\sqrt{a}-6\right)}{\sqrt{a}}}{\frac{3a-12}{a}\left(a-2\sqrt{a}\right)}$$

Express \frac{3a-12}{a}\left(a-2\sqrt{a}\right) as a single fraction.

$$\frac{\frac{\left(a-4\right)\left(3\sqrt{a}-6\right)}{\sqrt{a}}}{\frac{\left(3a-12\right)\left(a-2\sqrt{a}\right)}{a}}$$

Divide \frac{\left(a-4\right)\left(3\sqrt{a}-6\right)}{\sqrt{a}} by \frac{\left(3a-12\right)\left(a-2\sqrt{a}\right)}{a} by multiplying \frac{\left(a-4\right)\left(3\sqrt{a}-6\right)}{\sqrt{a}} by the reciprocal of \frac{\left(3a-12\right)\left(a-2\sqrt{a}\right)}{a}.

$$\frac{\left(a-4\right)\left(3\sqrt{a}-6\right)a}{\sqrt{a}\left(3a-12\right)\left(a-2\sqrt{a}\right)}$$

Factor the expressions that are not already factored.

$$\frac{3\left(\sqrt{a}-2\right)a\left(a-4\right)}{3\left(\sqrt{a}-2\right)\left(\sqrt{a}\right)^{2}\left(a-4\right)}$$

Cancel out 3\left(\sqrt{a}-2\right)\left(a-4\right) in both numerator and denominator.

$$\frac{a}{\left(\sqrt{a}\right)^{2}}$$

Expand the expression.

$$\frac{a}{a}$$

Cancel out a in both numerator and denominator.

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Factor

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