Question

Express each of the following as a fraction in its simplest form

if u answer for points,
I will take revenge by doing the same on your questions.

Answer 1

a) (8y + 9)/15.

b) (5x + 10)/8.

Explanation:

(a) y/3 + (y + 3)/5

The LCD of 3 and 5 is 15 so we have:

5y/15 + 3(y + 3)/15

= (5y + 3(y + 3)) / 15

= (5y + 3y + 9)/15

= (8y + 9)/15.

b) 3x/8 + (x + 5)/4

The LCD of 4 and 8 is 8 so we have:

3x/8 + 2(x + 5)/8

= (3x + 2x + 10) / 8

= (5x + 10)/8.

Answer 2

see explanation

Explanation:

(a)

Given

`(y)/(3)` +
`(y+3)/(5)`

The common denominator is 15 ( the LCM of 3 and 5 )

Multiply numerator/ denominator of first fraction by 5

Multiply the numerator/ denominator of second fraction by 3

=
`(5y)/(15)` +
`(3y+9)/(15)` ← add numerators , leaving denominator of 15

=
`(5y+3y+9)/(15)`

=
`(8y+9)/(15)`

(b)

Given

`(3x)/(8)` -
`(x+5)/(4)`

The common denominator is 8 ( the LCM of 8 and 4 )

Multiply numerator/ denominator of second fraction by 2

=
`(3x)/(8)` -
`(2(x+5))/(8)` ← simplify numerators leaving denominator of 8

=
`(3x-2x-10)/(8)`

=
`(x-10)/(8)`