Question

X and y simplifying problem. Please explain how to do thiese. I will gove 15 points

Answer 1

`\frac 56 x + \frac25 y - \frac14 x + \frac3{10} y`

First, combine like terms:

`\left(\frac 56 - \frac14\right) x + \left(\frac25 + \frac3{10}\right)y`

Now just simplify the coefficients of x and y. We do this by converting each pair of fractions to ones with a common denominator. Then we can combine them easily.

`\frac56 - \frac14 = \frac56\cdot\frac22 - \frac14\cdot\frac33 = (5\cdot2)/(6\cdot2) - (1\cdot3)/(4\cdot3) = (10)/(12) - \frac3{12} = (10-3)/(12) = \frac7{12}`

`\frac25 + \frac3{10} = \frac25\cdot\frac22 + \frac3{10} = (2\cdot2)/(5\cdot2) + \frac3{10} = \frac4{10} + \frac3{10} = (4+3)/(10) = \frac7{10}`

So the simplified expression would be

`\frac7{12} x + \frac7{10} y`