# Problem of the Week

## Updated at Mar 4, 2024 2:14 PM

To get more practice in equation, we brought you this problem of the week:

How would you solve $$2+{(3-\frac{5}{u})}^{2}=\frac{34}{9}$$?

Check out the solution below!

$2+{(3-\frac{5}{u})}^{2}=\frac{34}{9}$

 1 Subtract $$2$$ from both sides.${(3-\frac{5}{u})}^{2}=\frac{34}{9}-2$2 Simplify  $$\frac{34}{9}-2$$  to  $$\frac{16}{9}$$.${(3-\frac{5}{u})}^{2}=\frac{16}{9}$3 Take the square root of both sides.$3-\frac{5}{u}=\pm \sqrt{\frac{16}{9}}$4 Simplify  $$\sqrt{\frac{16}{9}}$$  to  $$\frac{\sqrt{16}}{\sqrt{9}}$$.$3-\frac{5}{u}=\pm \frac{\sqrt{16}}{\sqrt{9}}$5 Since $$4\times 4=16$$, the square root of $$16$$ is $$4$$.$3-\frac{5}{u}=\pm \frac{4}{\sqrt{9}}$6 Since $$3\times 3=9$$, the square root of $$9$$ is $$3$$.$3-\frac{5}{u}=\pm \frac{4}{3}$7 Break down the problem into these 2 equations.$3-\frac{5}{u}=\frac{4}{3}$$3-\frac{5}{u}=-\frac{4}{3}$8 Solve the 1st equation: $$3-\frac{5}{u}=\frac{4}{3}$$.1 Subtract $$3$$ from both sides.$-\frac{5}{u}=\frac{4}{3}-3$2 Simplify  $$\frac{4}{3}-3$$  to  $$-\frac{5}{3}$$.$-\frac{5}{u}=-\frac{5}{3}$3 Multiply both sides by $$u$$.$-5=-\frac{5}{3}u$4 Simplify  $$\frac{5}{3}u$$  to  $$\frac{5u}{3}$$.$-5=-\frac{5u}{3}$5 Multiply both sides by $$3$$.$-5\times 3=-5u$6 Simplify  $$-5\times 3$$  to  $$-15$$.$-15=-5u$7 Divide both sides by $$-5$$.$\frac{-15}{-5}=u$8 Two negatives make a positive.$\frac{15}{5}=u$9 Simplify  $$\frac{15}{5}$$  to  $$3$$.$3=u$10 Switch sides.$u=3$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$u=3$9 Solve the 2nd equation: $$3-\frac{5}{u}=-\frac{4}{3}$$.1 Subtract $$3$$ from both sides.$-\frac{5}{u}=-\frac{4}{3}-3$2 Simplify  $$-\frac{4}{3}-3$$  to  $$-\frac{13}{3}$$.$-\frac{5}{u}=-\frac{13}{3}$3 Multiply both sides by $$u$$.$-5=-\frac{13}{3}u$4 Simplify  $$\frac{13}{3}u$$  to  $$\frac{13u}{3}$$.$-5=-\frac{13u}{3}$5 Multiply both sides by $$3$$.$-5\times 3=-13u$6 Simplify  $$-5\times 3$$  to  $$-15$$.$-15=-13u$7 Divide both sides by $$-13$$.$\frac{-15}{-13}=u$8 Two negatives make a positive.$\frac{15}{13}=u$9 Switch sides.$u=\frac{15}{13}$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$u=\frac{15}{13}$10 Collect all solutions.$u=3,\frac{15}{13}$DoneDecimal Form: 3, 1.153846u=3,15/13