Add (4x)/(12y^2)+(5x)/(8y)

Math
4x12y2+5x8y
Cancel the common factor of 4 and 12.
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Factor 4 out of 4x.
4(x)12y2+5x8y
Cancel the common factors.
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Factor 4 out of 12y2.
4(x)4(3y2)+5x8y
Cancel the common factor.
4×4(3y2)+5x8y
Rewrite the expression.
x3y2+5x8y
x3y2+5x8y
x3y2+5x8y
To write x3y2 as a fraction with a common denominator, multiply by 88.
x3y2⋅88+5x8y
To write 5x8y as a fraction with a common denominator, multiply by 3y3y.
x3y2⋅88+5x8y⋅3y3y
Write each expression with a common denominator of 24y2, by multiplying each by an appropriate factor of 1.
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Multiply x3y2 and 88.
x⋅83y2⋅8+5x8y⋅3y3y
Multiply 8 by 3.
x⋅824y2+5x8y⋅3y3y
Multiply 5x8y and 3y3y.
x⋅824y2+5x(3y)8y(3y)
Multiply 3 by 8.
x⋅824y2+5x(3y)24y⋅y
Raise y to the power of 1.
x⋅824y2+5x(3y)24(y1y)
Raise y to the power of 1.
x⋅824y2+5x(3y)24(y1y1)
Use the power rule aman=am+n to combine exponents.
x⋅824y2+5x(3y)24y1+1
Add 1 and 1.
x⋅824y2+5x(3y)24y2
x⋅824y2+5x(3y)24y2
Combine the numerators over the common denominator.
x⋅8+5x(3y)24y2
Simplify the numerator.
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Factor x out of x⋅8+5x⋅3y.
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Factor x out of x⋅8.
x(8)+5x⋅3y24y2
Factor x out of 5x⋅3y.
x(8)+x(5⋅3y)24y2
Factor x out of x(8)+x(5⋅3y).
x(8+5⋅3y)24y2
x(8+5⋅3y)24y2
Multiply 5 by 3.
x(8+15y)24y2
x(8+15y)24y2
Add (4x)/(12y^2)+(5x)/(8y)

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