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Solving Rational Equations. LCD Method. Show work.


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

2 Answers

1 vote

Answer:


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

User Oliver Robie
by
8.3k points
5 votes

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)

User Massimo Callegari
by
8.2k points

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