Question

Can someone help me with the step by step solutions to these? Thanks​

Answer 1

c. √2/30

f. 13√3/14

i. -11√10/24

Explanation:

You want the sums of the fractions shown.

Sum of fractions

Two fractions can be added like this:

`(a)/(b)+(c)/(d)=(ad+bc)/(bd)`

If the denominators have a common factor (k), then this can be reduced to ...

`(a)/(bk)+(c)/(dk)=(ad+bc)/(bdk)`

The product bdk is the least common denominator when k is the greatest common factor.

Here, the numerators have a common factor, so we can factor that out, perform the sum, then multiply the result by that numerator factor.

c

`(√(2))/(5)-(√(2))/(6)=√(2)\left((1)/(5)-(1)/(6)\right)=√(2)\cdot(6-5)/(5\cdot6)=\boxed{(√(2))/(30)}`

f

`(3√(3))/(7)+(√(3))/(2)=√(3)\left((3)/(7)+(1)/(2)\right)=√(3)\cdot(3\cdot2+7)/(7\cdot2)=\boxed{(13√(3))/(14)}`

i

The denominators have a common factor of 2: 6=3·2, 8=4·2.

`(-5√(10))/(6)+(3√(10))/(8)=√(10)\left((-5)/(6)+(3)/(8)\right)=√(10)\cdot(-5\cdot4+3\cdot3)/(3\cdot4\cdot2)=\boxed{-(11√(10))/(24)}`