Algebra Demystified 2nd Ed

150 algebra De mystif ieD

Simplifying a fraction or adding two fractions sometimes only requires that we

factor –1 from one or more denominators. For instance, in yx

xy

−

−

the numerator

and denominator are only off by a factor of –1. To simplify this fraction, we

factor –1 from the numerator or denominator:

yx

xy

−

−

=^ −− +

−

=−−

−

()yx ()=− =−

xy

xy

xy

1

1

1 or yx

xy

yx

xy

yx

yx

−

−

= −

−− +

= −

−−

=

−

=−

()()

1

1

1.

In the sum^3

yx

x

− xy

+

−

the denominators are off by a factor of –1. Factor –1

from one of the denominators and use the fact that a

b

a

− b

=− to write both

terms with the same denominator.

33 33

yx

x

xy yx

x

xy xy

x

xy xy

x

− xy

+

−

=

−− +

+

−

=

−−

+

−

= −

−

+

() () −

==−+

−

3 x

xy

EXAMPLES

Factor –1 from the denominator and move the negative sign to the

numerator.

1

1

1

1

1

1

1

− 1

=

−−+

=

−−

= −

xx()()xx−

3

6

3

6

3

−− 6

=

−+

= −

xx()x+

−

+

= −

−− −

= −−

−−

=

−−

3

14 9

3

14 9

3

14 9

3

14 9

x

x

x

x

x

x

x

() x

()

16 5

73

16 5

73

16 5

37

16 5

3

x

x

x

x

x

x

− x

−

= −

−− +

= −

−−

=−−

()()−

()

77

16 5

x 37

x

x

=−+

−

PRACTICE

Factor –1 from the denominator and move the negative sign to the

numerator.

1.^1
yx−

=

2.^16
4 −

=

x

EXAMPLES

Factor –1 from the denominator and move the negative sign to the

PRACTICE

Factor –1 from the denominator and move the negative sign to the