Maths-
General
Easy

Question

Express the following as a rational expression in its lowest terms .
fraction numerator begin display style fraction numerator 2 x squared plus 6 x over denominator 3 x squared plus 7 x plus 2 end fraction end style over denominator begin display style fraction numerator x squared plus x minus 6 over denominator 3 x squared plus 7 x plus 2 end fraction end style end fraction

hintHint:

Simplify means to make it simple. In mathematics, simplify is the reduction of an expression/fraction into irreducible forms.
We are asked to reduce the expression into the lowest form.

The correct answer is: the expression in the lowest form is , 2x / (x - 2)


    Step 1 of 2:
    The given expression is, fraction numerator begin display style fraction numerator 2 x squared plus 6 x over denominator 3 x squared plus 7 x plus 2 end fraction end style over denominator begin display style fraction numerator x squared plus x minus 6 over denominator 3 x squared plus 7 x plus 2 end fraction end style end fraction
    Take the reciprocal of the second expression and multiply it with the first one. This procedure has the same effect as division.
    fraction numerator 2 x squared plus 6 x over denominator 3 x squared plus 7 x plus 2 end fraction cross times fraction numerator 3 x squared plus 7 x plus 2 over denominator x squared plus x minus 6 end fraction
    Step 2 of 2:
    Simplify the expression and cancel out the common factors;
    fraction numerator 2 x squared plus 6 x over denominator 3 x squared plus 7 x plus 2 end fraction cross times fraction numerator 3 x squared plus 7 x plus 2 over denominator x squared plus x minus 6 end fraction equals fraction numerator 2 x left parenthesis x plus 3 right parenthesis over denominator 3 x squared plus 7 x plus 2 end fraction cross times fraction numerator 3 x squared plus 7 x plus 2 over denominator x squared plus 3 x minus 2 x minus 6 end fraction
    equals fraction numerator 2 x left parenthesis x plus 3 right parenthesis over denominator 1 end fraction cross times fraction numerator 1 over denominator x left parenthesis x plus 3 right parenthesis minus 2 left parenthesis x plus 3 right parenthesis end fraction
    equals fraction numerator 2 x left parenthesis x plus 3 right parenthesis over denominator left parenthesis x minus 2 right parenthesis left parenthesis x plus 3 right parenthesis end fraction
    equals fraction numerator 2 x over denominator left parenthesis x minus 2 right parenthesis end fraction
    Thus, the expression in the lowest form is, equals fraction numerator 2 x over denominator left parenthesis x minus 2 right parenthesis end fraction

    Dividing an expression with the other expression and multiplying it with the reciprocal of the second expression has the same effect.

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