Simplify [1÷(x2+3x+2)]+[1÷(x2+5x+6)]

Question 1 Report

Simplify $[1 \div (x^{2} + 3 x + 2)] + [1 \div (x^{2} + 5 x + 6)]$

\frac{2}{(x + 1)^{2}}

\frac{2}{(x + 1) (x + 2}

\frac{2}{(x + 1) (x + 2}

\frac{2}{(x + 1) (x + 3}

Answer Details

$[1 \div (x^{2} + 3 x + 2)] + [1 \div (x^{2} + 5 x + 6)]$
= $1 \div (x^{2} + 3 x + 2) + [1 \div (x^{2} + 5 x + 6)]$
= $[1 \div ((x^{2} + x) + (2 x + 2))] + [1 \div ((x^{2} + 3 x) + (2 x + 6))]$
= [1 ÷ (x(x + 2) + 2(x +1))] + [1 ÷ (x(x + 3) +2(x + 3) )]
= [1 ÷ (x + 1)(x + 2)] + [1 ÷ ((x + 3) + (x + 2))]
=((x + 3) + (x + 1)) ÷ (x + 1)(x + 2)(x + 3)
Using the L.C.M
=((x + x + 3 + 1)) ÷ (x + 1)(x + 2)(x + 3)
=(2x+4)/(x+1)(x+2)(x+3) =2(x+2)/(x+1)(x+2)(x+3)
= $\frac{2}{(x + 1) (x + 3)}$

Read lesson note on Algebraic Fractions (WAEC)

Algebraic Fractions

View Answer

Related Questions

Download The App On Google Playstore