Answer:
B. [tex]\dfrac{1}{3}x-\dfrac{1}{4}y-\dfrac{4}{5}+\dfrac{1}{3}x-\dfrac{1}{4}y[/tex]
Step-by-step explanation:
Consider all options:
A. In the expression
[tex]\dfrac{1}{3}x-\dfrac{1}{4}y-\dfrac{4}{5}+\dfrac{1}{3}x+\dfrac{1}{4}y[/tex]
combine the like terms:
[tex]\left(\dfrac{1}{3}x+\dfrac{1}{3}x\right)+\left(-\dfrac{1}{4}y+\dfrac{1}{4}y\right)-\dfrac{4}{5}[/tex]
Use distributive property:
[tex]x\left(\dfrac{1}{3}+\dfrac{1}{3}\right)+y\left(-\dfrac{1}{4}+\dfrac{1}{4}\right)-\dfrac{4}{5}=\dfrac{2}{3}x-\dfrac{4}{5}[/tex]
This option is false.
2. In the expression
[tex]\dfrac{1}{3}x-\dfrac{1}{4}y-\dfrac{4}{5}+\dfrac{1}{3}x-\dfrac{1}{4}y[/tex]
combine the like terms:
[tex]\left(\dfrac{1}{3}x+\dfrac{1}{3}x\right)+\left(-\dfrac{1}{4}y-\dfrac{1}{4}y\right)-\dfrac{4}{5}[/tex]
Use distributive property:
[tex]x\left(\dfrac{1}{3}+\dfrac{1}{3}\right)+y\left(-\dfrac{1}{4}-\dfrac{1}{4}\right)-\dfrac{4}{5}=\dfrac{2}{3}x-\dfrac{1}{2}y-\dfrac{4}{5}[/tex]
This option is true.
3. In the expression
[tex]\dfrac{1}{3}x-\dfrac{1}{4}y-\dfrac{1}{5}-\dfrac{1}{3}x-\dfrac{3}{5}-\dfrac{1}{4}y[/tex]
combine the like terms:
[tex]\left(\dfrac{1}{3}x-\dfrac{1}{3}x\right)+\left(-\dfrac{1}{4}y-\dfrac{1}{4}y\right)+\left(-\dfrac{1}{5}-\dfrac{3}{5}\right)[/tex]
Use distributive property:
[tex]x\left(\dfrac{1}{3}-\dfrac{1}{3}\right)+y\left(-\dfrac{1}{4}-\dfrac{1}{4}\right)-\dfrac{4}{5}=-\dfrac{1}{2}y-\dfrac{4}{5}[/tex]
This option is false.
4. In the expression
[tex]\dfrac{1}{3}x-\dfrac{1}{4}y+\dfrac{2}{5}+\dfrac{1}{3}x-\dfrac{2}{5}-\dfrac{1}{4}y[/tex]
combine the like terms:
[tex]\left(\dfrac{1}{3}x+\dfrac{1}{3}x\right)+\left(-\dfrac{1}{4}y-\dfrac{1}{4}y\right)+\left(\dfrac{2}{5}-\dfrac{2}{5}\right)[/tex]
Use distributive property:
[tex]x\left(\dfrac{1}{3}+\dfrac{1}{3}\right)+y\left(-\dfrac{1}{4}-\dfrac{1}{4}\right)=\dfrac{2}{3}x-\dfrac{1}{2}y[/tex]
This option is false.
