Given:
The expression is:
![-\dfrac{1}{4}-\left(\dfrac{2}{5}+\dfrac{3}{7}\right)](https://tex.z-dn.net/?f=-%5Cdfrac%7B1%7D%7B4%7D-%5Cleft%28%5Cdfrac%7B2%7D%7B5%7D%2B%5Cdfrac%7B3%7D%7B7%7D%5Cright%29)
To find:
The expression that is equivalent to the given expression.
Solution:
We have,
![-\dfrac{1}{4}-\left(\dfrac{2}{5}+\dfrac{3}{7}\right)](https://tex.z-dn.net/?f=-%5Cdfrac%7B1%7D%7B4%7D-%5Cleft%28%5Cdfrac%7B2%7D%7B5%7D%2B%5Cdfrac%7B3%7D%7B7%7D%5Cright%29)
Using the distributive property, we get
![=-\dfrac{1}{4}-\dfrac{2}{5}-\dfrac{3}{7}](https://tex.z-dn.net/?f=%3D-%5Cdfrac%7B1%7D%7B4%7D-%5Cdfrac%7B2%7D%7B5%7D-%5Cdfrac%7B3%7D%7B7%7D)
Taking LCM, we get
![=\dfrac{-35-56-60}{140}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B-35-56-60%7D%7B140%7D)
![=\dfrac{-151}{140}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B-151%7D%7B140%7D)
Therefore, the expression
is equivalent to the given expression expression.
Note: There are more than one equivalent expressions.