# Simplify 0.25y+1/(4y)+0.5

0.25y+14y+0.5
To write 0.25y as a fraction with a common denominator, multiply by 4y4y.
0.25y⋅4y4y+14y+0.5
Simplify terms.
Combine 0.25y and 4y4y.
0.25y(4y)4y+14y+0.5
Combine the numerators over the common denominator.
0.25y(4y)+14y+0.5
0.25y(4y)+14y+0.5
Simplify the numerator.
Factor 0.25 out of 0.25y(4y)+1.
Move y.
0.25⋅4y⋅y+14y+0.5
Factor 0.25 out of 0.25⋅4y⋅y.
0.25(4y⋅y)+14y+0.5
Factor 0.25 out of 1.
0.25(4y⋅y)+0.25(4)4y+0.5
Factor 0.25 out of 0.25(4y⋅y)+0.25(4).
0.25(4y⋅y+4)4y+0.5
0.25(4y⋅y+4)4y+0.5
Factor 4 out of 4y⋅y+4.
Factor 4 out of 4y⋅y.
0.25(4(y⋅y)+4)4y+0.5
Factor 4 out of 4.
0.25(4(y⋅y)+4(1))4y+0.5
Factor 4 out of 4(y⋅y)+4(1).
0.25(4(y⋅y+1))4y+0.5
0.25(4(y⋅y+1))4y+0.5
Multiply y by y.
0.25⋅4(y2+1)4y+0.5
Combine exponents.
Multiply 0.25 by 4.
1(y2+1)4y+0.5
Multiply y2+1 by 1.
y2+14y+0.5
y2+14y+0.5
y2+14y+0.5
To write 0.5 as a fraction with a common denominator, multiply by 4y4y.
y2+14y+0.5⋅4y4y
Simplify terms.
Combine 0.5 and 4y4y.
y2+14y+0.5(4y)4y
Combine the numerators over the common denominator.
y2+1+0.5(4y)4y
y2+1+0.5(4y)4y
Factor using the perfect square rule.
Rearrange terms.
y2+0.5(4y)+14y
Rewrite 1 as 12.
y2+0.5(4y)+124y
Check the middle term by multiplying 2ab and compare this result with the middle term in the original expression.
2ab=2⋅y⋅1
Simplify.
2ab=2y
Factor using the perfect square trinomial rule a2+2ab+b2=(a+b)2, where a=y and b=1.
(y+1)24y
(y+1)24y
Simplify 0.25y+1/(4y)+0.5

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