Solving Rational Equations. LCD Method. Show work.[tex]\frac{3}{5x} + \frac{7}{2x} =1[/tex]

Answer: [tex]x=\frac{41}{10}[/tex]Step-by-step explanation: Descompose the denominators into their prime factors to calculate the Least Common Denominator (LCD): [tex]5x=5*x[/tex] [tex]2=2*x[/tex] Choose the common and non-common numbers and varibles with the largest exponents and multiply them: [tex]LCD=5*2*x=10x[/tex] Divide eac originl denominator by the LCD and multiply the resul by each numerator. Then, make the addition and solve for x: [tex]\frac{3(2)+7(5)}{10x}=1\\\\\frac{6+35}{10x}=1\\\\\frac{41}{10x}=1\\\\41=10x\\x=\frac{41}{10}[/tex]