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Division of Algebraic Fractions

To solve the problems on division of algebraic fractions we will follow the same rules that we already learnt in dividing fractions in arithmetic.

From division of fractions we know,

First fraction ÷ Second fraction = First fraction × 1Secondfraction

In algebraic fractions, the quotient can be determined in the same way i.e.

First algebraic fraction ÷ Second algebraic fraction

                               = First algebraic fraction × 1Secondalgebraicfraction


1. Determine the quotient of the algebraic fractions: p2r2q2s2÷qrps

Solution:

p2r2q2s2÷qrps

= p2r2q2s2×psqr

= p2r2psq2s2qr

= p3r2sq3rs2

In the numerator and denominator of the quotient, the common factor is ‘rs’ by which if the numerator and denominator are divided, its lowest form will be = p3rq3s


2. Find the quotient of the algebraic fractions: x(y+z)y2z2÷y+zyz

Solution:

x(y+z)y2z2÷y+zyz

= x(y+z)y2z2×yzy+z

= x(y+z)(y+z)(yz)×yzy+z

= x(y+z)(yz)(y+z)(yz)(y+z)

= x(y+z)(yz)(y+z)(yz)(y+z)

We observe that the common factor in the numerator and denominator of the quotient is (y + z) (y – z) by which, if the numerator and the denominator are divided, its lowest form will be xy+z.


3. Divide the algebraic fractions and express in the lowest form:

m2m6m2+4m5÷m24m+3m2+6m+5

Solution:

m2m6m2+4m5÷m24m+3m2+6m+5

= m2m6m2+4m5×m2+6m+5m24m+3

= m23m+2m6m2+5mm5×m2+5m+m+5m23mm+3

= m(m3)+2(m3)m(m+5)1(m+5)×m(m+5)+1(m+5)m(m3)1(m3)

= (m3)(m+2)(m+5)(m1)×(m+5)(m+1)(m3)(m1)

= (m3)(m+2)(m+5)(m+1)(m+5)(m1)(m3)(m1)

= (m3)(m+2)(m+5)(m+1)(m+5)(m1)(m3)(m1)

We observe that the common factor in the numerator and denominator of the quotient is (m - 3) (m + 5), by which if the numerator and the denominator of the quotient is divided, (m+2)(m+1)(m1)(m1) i.e. (m+2)(m+1)(m1)2 will be its reduced lowest form.







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