Solve p*q=sqrt{8040}(p+q)

$$p \cdot q = \sqrt { 8040 } ( p + q )$$

Solve for p

$$p=\frac{2\sqrt{2010}q}{q-2\sqrt{2010}}$$

$$q\neq 2\sqrt{2010}$$

Steps for Solving Linear Equation

Factor 8040=2^{2}\times 2010. Rewrite the square root of the product \sqrt{2^{2}\times 2010} as the product of square roots \sqrt{2^{2}}\sqrt{2010}. Take the square root of 2^{2}.

$$pq=2\sqrt{2010}\left(p+q\right)$$

Use the distributive property to multiply 2\sqrt{2010} by p+q.

$$pq=2\sqrt{2010}p+2\sqrt{2010}q$$

Subtract 2\sqrt{2010}p from both sides.

$$pq-2\sqrt{2010}p=2\sqrt{2010}q$$

Combine all terms containing p.

$$\left(q-2\sqrt{2010}\right)p=2\sqrt{2010}q$$

Divide both sides by q-2\sqrt{2010}.

$$\frac{\left(q-2\sqrt{2010}\right)p}{q-2\sqrt{2010}}=\frac{2\sqrt{2010}q}{q-2\sqrt{2010}}$$

Dividing by q-2\sqrt{2010} undoes the multiplication by q-2\sqrt{2010}.

$$p=\frac{2\sqrt{2010}q}{q-2\sqrt{2010}}$$

Solve for q

$$q=\frac{2\sqrt{2010}p}{p-2\sqrt{2010}}$$

$$p\neq 2\sqrt{2010}$$

Steps for Solving Linear Equation

Factor 8040=2^{2}\times 2010. Rewrite the square root of the product \sqrt{2^{2}\times 2010} as the product of square roots \sqrt{2^{2}}\sqrt{2010}. Take the square root of 2^{2}.

$$pq=2\sqrt{2010}\left(p+q\right)$$

Use the distributive property to multiply 2\sqrt{2010} by p+q.

$$pq=2\sqrt{2010}p+2\sqrt{2010}q$$

Subtract 2\sqrt{2010}q from both sides.

$$pq-2\sqrt{2010}q=2\sqrt{2010}p$$

Combine all terms containing q.

$$\left(p-2\sqrt{2010}\right)q=2\sqrt{2010}p$$

Divide both sides by p-2\sqrt{2010}.

$$\frac{\left(p-2\sqrt{2010}\right)q}{p-2\sqrt{2010}}=\frac{2\sqrt{2010}p}{p-2\sqrt{2010}}$$

Dividing by p-2\sqrt{2010} undoes the multiplication by p-2\sqrt{2010}.

$$q=\frac{2\sqrt{2010}p}{p-2\sqrt{2010}}$$