Question

Write each expression as one simplified fraction. Format should be (answer) if … . For example: x > 2 if x does not equal to 0.

A) (a - 2) / 8a + (2a + 5) / 8a - (3 - a) / 8a


B) (5a + b^2) / 8b - (5a - 7b^2) / 8b


C) (b - 2)^2 / (2-b)^2


D) (7b - 14b^2) / (42b^2 - 21b)


E) (25 - a^2) / (3a - 15)

Answer 1

a. the simplified expression is 1/2

b. the simplified expression is b

c the simplified expression is
`\frac{{(b - 2)^2}}{{(2 - b)^2}}`

d. the simplified expression is (1 - 2b)/(2b - 1)

e. simplified expression is -(a + 5) /3

How to simplify the expressions

A)
`(\frac{{(a - 2)}}{{8a}} + \frac{{(2a + 5)}}{{8a}} - \frac{{(3 - a)}}{{8a}}`

Combine the numerators over the common denominator

`\frac{{a - 2 + 2a + 5 - (3 - a)}}{{8a}}`

Combine like terms:

`\frac{{4a}}{{8a}}`

= 1/2

B)
`\frac{{5a + b^2}}{{8b}} - \frac{{5a - 7b^2}}{{8b}}`

Similar method results to

=
`\frac{{(5a + b^2) - (5a - 7b^2)}}{{8b}}`

=
`\frac{{8b^2}}{{8b}}`

= b

C
`\frac{{(b - 2)^2}}{{(2 - b)^2}}`

This expression is already simplified

D.
`\frac{{7b - 14b^2}}{{42b^2 - 21b}}`

=
`\frac{{7b(1 - 2b)}}{{21b(2b - 1)}}`

=
`\frac{{1 - 2b}}{{2b - 1}}`

E
`\frac{{25 - a^2}}{{3a - 15}}`

=
`\frac{{(5 + a)(5 - a)}}{{3(a - 5)}}`

=
`\frac{{5 + a}}{{-3}}`