Question

Simplifying Complex fractions using any method

Answer 1

3ab/(b+a)

Explanation:

Simplifying the numerator:

3/a - 3/b

3[1/a - 1/b]

Lcm is ab

3[(b - a)/ab]

Simplifying the denominator:

1/a² - 1/b²

Lcm: a²b²

(b² - a²)/(a²b²)

(b - a)(b + a)/(a²b²)

Numerator ÷ denominator

3[(b - a)/ab] ÷ (b - a)(b + a)/(a²b²)

3[(b - a)/ab] × a²b²/[(b - a)(b + a)]

3ab/(b + a)

Answer 2

3ab

-------------------

(b+a)

Explanation:

3/a - 3/b

-------------------

1/a^2 - 1/b^2

Multiply the top and bottom by a^2 b^2/ a^2/b^2 to clear the fractions

(3/a - 3/b) a^2 b^2

-------------------

(1/a^2 - 1/b^2) a^2b^2

3ab^2 - 3 a^2 b

-------------------

b^2 - a^2

Factor out 3ab on the top

3ab( b-a)

-------------------

b^2 - a^2

The bottom is the difference of squares

3ab( b-a)

-------------------

(b-a) (b+a)

Cancel like terms from the top and bottom

3ab

-------------------

(b+a)