A balancing act is a situation in which someone has to give attention to two different things at the same time (it has its origins in circus acts).
The life of a modern parent is a balancing act of going out to work and raising children at home.
My sisters are always fighting between themselves. Keeping the peace at home is a balancing act.
To balance something against something else means to compare the value of something in relation to something else.
During a recession a government has to balance the needs of the poorest against the wishes of the richest.
Elephants are very intelligent, sociable animals. They live in groups led by the oldest female, or matriarch. An elephant’s skin is so sensitive it can feel a fly landing.