# Solve for p 1/(3p+1)=4/(9p+2)

13p+1=49p+2
Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.
1⋅(9p+2)=(3p+1)⋅4
Solve the equation for p.
Multiply 9p+2 by 1.
9p+2=(3p+1)⋅4
Simplify (3p+1)⋅4.
Apply the distributive property.
9p+2=3p⋅4+1⋅4
Multiply.
Multiply 4 by 3.
9p+2=12p+1⋅4
Multiply 4 by 1.
9p+2=12p+4
9p+2=12p+4
9p+2=12p+4
Move all terms containing p to the left side of the equation.
Subtract 12p from both sides of the equation.
9p+2-12p=4
Subtract 12p from 9p.
-3p+2=4
-3p+2=4
Move all terms not containing p to the right side of the equation.
Subtract 2 from both sides of the equation.
-3p=4-2
Subtract 2 from 4.
-3p=2
-3p=2
Divide each term by -3 and simplify.
Divide each term in -3p=2 by -3.
-3p-3=2-3
Cancel the common factor of -3.
Cancel the common factor.
-3p-3=2-3
Divide p by 1.
p=2-3
p=2-3
Move the negative in front of the fraction.
p=-23
p=-23
p=-23
The result can be shown in multiple forms.
Exact Form:
p=-23
Decimal Form:
p=-0.6‾
Solve for p 1/(3p+1)=4/(9p+2)

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