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Leni [432]
3 years ago
12

Solving Rational Equations. LCD Method. Show work.

rac%7B7%7D%7B2x%7D%20%3D1" id="TexFormula1" title="\frac{3}{5x} + \frac{7}{2x} =1" alt="\frac{3}{5x} + \frac{7}{2x} =1" align="absmiddle" class="latex-formula">
Mathematics
2 answers:
Strike441 [17]3 years ago
8 0

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}

Pepsi [2]3 years ago
7 0

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

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