DIVISION OF FRACTION –
To divide one algebraic fraction by another, multiply the first by the reciprocal of the second
w y
-------- ÷ --------
x z
w z wz
-------- X -------- = ----------- where x ≠ 0 & z ≠ 0
x y xy
There are some example are given below for your better understanding –
10aᶟb 15a²b²
Example.1) ---------- ÷ -----------
5xy⁴ 20x²yᶟ
10aᶟb 15a²b² 10aᶟb 20x²yᶟ
Ans.) ----------- ÷ ----------- = ----------- X -----------
5xy⁴ 20x²yᶟ 5xy⁴ 15a²b²
10 X 20 X a X a X a X b X x X x X y X y X y
= ------------------------------------------------
5 X 15 X x X y X y X y X y X a X a X b X b
2 X 4 X a X x 8ax
= ----------------- = ---------- (Ans.)
3 X y X b 3by
Alternatively,
10aᶟb 15a²b² 10aᶟb 20x²yᶟ
Ans.) --------- ÷ ---------- = ----------- X -----------
5xy⁴ 20x²yᶟ 5xy⁴ 15a²b²
10 X 20 X aᶟ X b X x² X yᶟ
= ------------------------------
5 X 15 X x X y⁴ X a² X b²
2 X 4 X aᶟ⁻² X x²⁻¹
= -----------------------
3 X y⁴⁻ᶟ X b²⁻¹
8 X a¹ X x¹ 8ax
= --------------- = ---------- (Ans.)
3 X y¹ X b¹ 3by
25a⁴b² 10a²b⁵
Example.2) ----------- ÷ ------------
15x²y⁴ 12x⁴y²
25a⁴b² 10a²b⁵ 25a⁴b² 12x⁴y²
Ans.) ---------- ÷ ----------- = ----------- X -----------
15x²y⁴ 12x⁴y² 15x²y⁴ 10a²b⁵
5 X 5 X 3 X 2 X 2 X a X a X a X a X b X b X x X x X x X x X y X y
= -----------------------------------------------------------
5 X 3 X 5 X 2 X x X x X y X y X y X y X a X a X b X b X b X b X b
2 X a X a X x X x 2a²x²
= --------------------- = ------------ (Ans.)
b X b X b X y X y bᶟy²
Alternatively,
25a⁴b² 10a²b⁵ 25a⁴b² 12x⁴y²
Ans.) ----------- ÷ ---------- = ----------- X -----------
15x²y⁴ 12x⁴y² 15x²y⁴ 10a²b⁵
5 X 5 X 3 X 2 X 2 X a⁴ X b² X x⁴ X y²
= ----------------------------------------
3 X 5 X 5 X 2 X x² X y⁴ X a² X b⁵
2 X a⁴⁻² X x⁴⁻² 2a²x²
= ------------------- = ------------ (Ans.)
y⁴⁻² X b⁵⁻² y²bᶟ