Question

Solving Rational Equations. LCD Method. Show work.

$\frac{3}{5x} + \frac{7}{2x} =1$

Answer 1

Answer: $x=\frac{41}{10}$

Step-by-step 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:

$\frac{3(2)+7(5)}{10x}=1\\\\\frac{6+35}{10x}=1\\\\\frac{41}{10x}=1\\\\41=10x\\x=\frac{41}{10}$

Answer 2

Answer:

$x=4.1$

Step-by-step explanation:

The given equation is;

$\frac{3}{5x}+\frac{7}{2x}=1$

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

$10x(\frac{3}{5x})+10x(\frac{7}{2x})=10x$

Cancel the common factors to obtain;

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

$6+35=10x$

$41=10x$

Divide by 10

$x=\frac{41}{10}$

$x=4.1$