Solve A=15,9/sqrt{5-sqrt{3}}+7/sqrt{5+sqrt{3}}

$$A = \frac { 15,9 } { \sqrt { 5 } - \sqrt { 3 } } + \frac { 7 } { \sqrt { 5 } + \sqrt { 3 } }$$

Solve for A

$$A = \frac{89 \sqrt{3} + 229 \sqrt{5}}{20} \approx 33.310604436$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{15,9}{\sqrt{5}-\sqrt{3}} by multiplying numerator and denominator by \sqrt{5}+\sqrt{3}.

$$A=\frac{15,9\left(\sqrt{5}+\sqrt{3}\right)}{\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\right)}+\frac{7}{\sqrt{5}+\sqrt{3}}$$

Consider \left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$A=\frac{15,9\left(\sqrt{5}+\sqrt{3}\right)}{\left(\sqrt{5}\right)^{2}-\left(\sqrt{3}\right)^{2}}+\frac{7}{\sqrt{5}+\sqrt{3}}$$

Square \sqrt{5}. Square \sqrt{3}.

$$A=\frac{15,9\left(\sqrt{5}+\sqrt{3}\right)}{5-3}+\frac{7}{\sqrt{5}+\sqrt{3}}$$

Subtract 3 from 5 to get 2.

$$A=\frac{15,9\left(\sqrt{5}+\sqrt{3}\right)}{2}+\frac{7}{\sqrt{5}+\sqrt{3}}$$

Divide 15,9\left(\sqrt{5}+\sqrt{3}\right) by 2 to get 7,95\left(\sqrt{5}+\sqrt{3}\right).

$$A=7,95\left(\sqrt{5}+\sqrt{3}\right)+\frac{7}{\sqrt{5}+\sqrt{3}}$$

Use the distributive property to multiply 7,95 by \sqrt{5}+\sqrt{3}.

$$A=7,95\sqrt{5}+7,95\sqrt{3}+\frac{7}{\sqrt{5}+\sqrt{3}}$$

Rationalize the denominator of \frac{7}{\sqrt{5}+\sqrt{3}} by multiplying numerator and denominator by \sqrt{5}-\sqrt{3}.

$$A=7,95\sqrt{5}+7,95\sqrt{3}+\frac{7\left(\sqrt{5}-\sqrt{3}\right)}{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}$$

Consider \left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$A=7,95\sqrt{5}+7,95\sqrt{3}+\frac{7\left(\sqrt{5}-\sqrt{3}\right)}{\left(\sqrt{5}\right)^{2}-\left(\sqrt{3}\right)^{2}}$$

Square \sqrt{5}. Square \sqrt{3}.

$$A=7,95\sqrt{5}+7,95\sqrt{3}+\frac{7\left(\sqrt{5}-\sqrt{3}\right)}{5-3}$$

Subtract 3 from 5 to get 2.

$$A=7,95\sqrt{5}+7,95\sqrt{3}+\frac{7\left(\sqrt{5}-\sqrt{3}\right)}{2}$$

Use the distributive property to multiply 7 by \sqrt{5}-\sqrt{3}.

$$A=7,95\sqrt{5}+7,95\sqrt{3}+\frac{7\sqrt{5}-7\sqrt{3}}{2}$$

Divide each term of 7\sqrt{5}-7\sqrt{3} by 2 to get \frac{7}{2}\sqrt{5}-\frac{7}{2}\sqrt{3}.

$$A=7,95\sqrt{5}+7,95\sqrt{3}+\frac{7}{2}\sqrt{5}-\frac{7}{2}\sqrt{3}$$

Combine 7,95\sqrt{5} and \frac{7}{2}\sqrt{5} to get \frac{229}{20}\sqrt{5}.

$$A=\frac{229}{20}\sqrt{5}+7,95\sqrt{3}-\frac{7}{2}\sqrt{3}$$

Combine 7,95\sqrt{3} and -\frac{7}{2}\sqrt{3} to get \frac{89}{20}\sqrt{3}.

$$A=\frac{229}{20}\sqrt{5}+\frac{89}{20}\sqrt{3}$$

Assign A

$$A≔\frac{89\sqrt{3}+229\sqrt{5}}{20}$$