Solve x=frac{10sqrt{3}+10sqrt{2}}{sqrt{3}+sqrt{2}}

$$x= \frac{ 10 \sqrt{ 3 } +10 \sqrt{ 2 } }{ \sqrt{ 3 } + \sqrt{ 2 } }$$

Solve for x

$$x=10$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{10\sqrt{3}+10\sqrt{2}}{\sqrt{3}+\sqrt{2}} by multiplying numerator and denominator by \sqrt{3}-\sqrt{2}.

$$x=\frac{\left(10\sqrt{3}+10\sqrt{2}\right)\left(\sqrt{3}-\sqrt{2}\right)}{\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{3}-\sqrt{2}\right)}$$

Consider \left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{3}-\sqrt{2}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$x=\frac{\left(10\sqrt{3}+10\sqrt{2}\right)\left(\sqrt{3}-\sqrt{2}\right)}{\left(\sqrt{3}\right)^{2}-\left(\sqrt{2}\right)^{2}}$$

Square \sqrt{3}. Square \sqrt{2}.

$$x=\frac{\left(10\sqrt{3}+10\sqrt{2}\right)\left(\sqrt{3}-\sqrt{2}\right)}{3-2}$$

Subtract 2 from 3 to get 1.

$$x=\frac{\left(10\sqrt{3}+10\sqrt{2}\right)\left(\sqrt{3}-\sqrt{2}\right)}{1}$$

Anything divided by one gives itself.

$$x=\left(10\sqrt{3}+10\sqrt{2}\right)\left(\sqrt{3}-\sqrt{2}\right)$$

Apply the distributive property by multiplying each term of 10\sqrt{3}+10\sqrt{2} by each term of \sqrt{3}-\sqrt{2}.

$$x=10\left(\sqrt{3}\right)^{2}-10\sqrt{3}\sqrt{2}+10\sqrt{2}\sqrt{3}-10\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{3} is 3.

$$x=10\times 3-10\sqrt{3}\sqrt{2}+10\sqrt{2}\sqrt{3}-10\left(\sqrt{2}\right)^{2}$$

Multiply 10 and 3 to get 30.

$$x=30-10\sqrt{3}\sqrt{2}+10\sqrt{2}\sqrt{3}-10\left(\sqrt{2}\right)^{2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$x=30-10\sqrt{6}+10\sqrt{2}\sqrt{3}-10\left(\sqrt{2}\right)^{2}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$x=30-10\sqrt{6}+10\sqrt{6}-10\left(\sqrt{2}\right)^{2}$$

Combine -10\sqrt{6} and 10\sqrt{6} to get 0.

$$x=30-10\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$x=30-10\times 2$$

Multiply -10 and 2 to get -20.

$$x=30-20$$

Subtract 20 from 30 to get 10.

$$x=10$$

Assign x

$$x≔10$$