Answer:
The difference between the heights of the Birch and Spruce trees is:
![(3)/(8)\ units](https://img.qammunity.org/2019/formulas/mathematics/middle-school/yf28iwfs4d33v0hgrzv8peftzk5zgkxjsd.png)
Explanation:
The height of the Birch tree is:
which in improper fraction is written as:
![(13)/(4)\ units](https://img.qammunity.org/2019/formulas/mathematics/middle-school/5mf20pvsg42ou3udq4bos54t4189rpgsoa.png)
Also, the height of Spruce tree is:
which in improper fraction is written as:
![(23)/(8)\ units](https://img.qammunity.org/2019/formulas/mathematics/middle-school/hkwrvhz3laxvxo7srjy6crirjquxpcg37h.png)
The difference in the height of two tree is given by:
![(13)/(4)-(23)/(8)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/3rcck5zq97mll4ja4nw4avo8oplj2l8c3y.png)
on taking least common multiple we get:
![=(13* 2-23* 1)/(8)\\\\=(26-23)/(8)\\\\\\=(3)/(8)\ units](https://img.qammunity.org/2019/formulas/mathematics/middle-school/qugxos39pvijotix7upi68q3se32caium3.png)
Hence, the difference between the height of tree is:
![(3)/(8)\ units](https://img.qammunity.org/2019/formulas/mathematics/middle-school/yf28iwfs4d33v0hgrzv8peftzk5zgkxjsd.png)