Question

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

Answer 1

$\dfrac 56 x + \dfrac25 y - \dfrac14 x + \dfrac3{10} y$

First, combine like terms:

$\left(\dfrac 56 - \dfrac14\right) x + \left(\dfrac25 + \dfrac3{10}\right)y$

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.

$\dfrac56 - \dfrac14 = \dfrac56\cdot\dfrac22 - \dfrac14\cdot\dfrac33 = \dfrac{5\cdot2}{6\cdot2} - \dfrac{1\cdot3}{4\cdot3} = \dfrac{10}{12} - \dfrac3{12} = \dfrac{10-3}{12} = \dfrac7{12}$

$\dfrac25 + \dfrac3{10} = \dfrac25\cdot\dfrac22 + \dfrac3{10} = \dfrac{2\cdot2}{5\cdot2} + \dfrac3{10} = \dfrac4{10} + \dfrac3{10} = \dfrac{4+3}{10} = \dfrac7{10}$

So the simplified expression would be

$\dfrac7{12} x + \dfrac7{10} y$