Question

How do you simplify `\frac { 5y ^ { 2} } { 6c k } + \frac { k ^ { 3} x ^ { 2} } { 8c ^ { 2} d }`?

Answer 1

`(20cdy^2+3k^4x^2)/(24c^2dk)`

Explanation:

it is
`\frac { 5y ^ { 2} } { 6c k }(\color(red)(\frac{4cd}{4cd})) + \frac { k ^ { 3} x ^ { 2} } { 8c ^ { 2} d }(\color(blue)(\frac{3k}{3k}))`

`\color(tomato)((20cdy^2)/(24c^2dk)+(3k^4x^2)/(24c^2dk))`

Note
Your common denominator comes from the fact that the LCM (least common multiple) of 6 and 8 being 24. The rest is just multiplying the variables.