Solving Rational Equations. LCD Method. Show work. (3)/(5x) + (7)/(2x) =1

Question

Solving Rational Equations. LCD Method. Show work.


`(3)/(5x) + (7)/(2x) =1`

Answer 1

`x=4.1`

Explanation:

The given equation is;

`(3)/(5x)+(7)/(2x)=1`

Multiply through by the Least Common Denominator which is
`-10x`

`10x((3)/(5x))+10x((7)/(2x))=10x`

Cancel the common factors to obtain;

`2(3)+5(7)=10x`

`6+35=10x`

`41=10x`

Divide by 10

`x=(41)/(10)`

`x=4.1`

Answer 2

Answer:
`x=(41)/(10)`

Explanation:

Descompose the denominators into their prime factors to calculate the Least Common Denominator (LCD):

`5x=5*x`

`2=2*x`

Choose the common and non-common numbers and varibles with the largest exponents and multiply them:

`LCD=5*2*x=10x`

Divide eac originl denominator by the LCD and multiply the resul by each numerator. Then, make the addition and solve for x:

`(3(2)+7(5))/(10x)=1\\\\(6+35)/(10x)=1\\\\(41)/(10x)=1\\\\41=10x\\x=(41)/(10)`