Simplify ( square root of u-5)/(5+ square root of u)

Math
u-55+u
Multiply u-55+u by 5-u5-u.
u-55+u⋅5-u5-u
Combine fractions.
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Multiply u-55+u and 5-u5-u.
(u-5)(5-u)(5+u)(5-u)
Expand the denominator using the FOIL method.
(u-5)(5-u)25-5u+u⋅5-u2
Simplify.
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Use axn=axn to rewrite u as u12.
(u-5)(5-u)25-(u12)2
Apply the power rule and multiply exponents, (am)n=amn.
(u-5)(5-u)25-u12⋅2
Combine 12 and 2.
(u-5)(5-u)25-u22
Cancel the common factor of 2.
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Cancel the common factor.
(u-5)(5-u)25-u22
Divide 1 by 1.
(u-5)(5-u)25-u1
(u-5)(5-u)25-u1
Simplify.
(u-5)(5-u)25-u
(u-5)(5-u)25-u
(u-5)(5-u)25-u
Simplify the numerator.
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Factor -1 out of u.
(-1(-u)-5)(5-u)25-u
Rewrite -5 as -1(5).
(-1(-u)-1(5))(5-u)25-u
Factor -1 out of -1(-u)-1(5).
-1(-u+5)(5-u)25-u
Reorder terms.
-1(5-u)(5-u)25-u
Raise 5-u to the power of 1.
-1((5-u)1(5-u))25-u
Raise 5-u to the power of 1.
-1((5-u)1(5-u)1)25-u
Use the power rule aman=am+n to combine exponents.
-1(5-u)1+125-u
Add 1 and 1.
-1(5-u)225-u
-1(5-u)225-u
Rewrite (5-u)2 as (5-u)(5-u).
-1((5-u)(5-u))25-u
Expand (5-u)(5-u) using the FOIL Method.
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Apply the distributive property.
-1(5(5-u)-u(5-u))25-u
Apply the distributive property.
-1(5⋅5+5(-u)-u(5-u))25-u
Apply the distributive property.
-1(5⋅5+5(-u)-u⋅5-u(-u))25-u
-1(5⋅5+5(-u)-u⋅5-u(-u))25-u
Simplify and combine like terms.
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Simplify each term.
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Multiply 5 by 5.
-1(25+5(-u)-u⋅5-u(-u))25-u
Multiply -1 by 5.
-1(25-5u-u⋅5-u(-u))25-u
Multiply 5 by -1.
-1(25-5u-5u-u(-u))25-u
Multiply -u(-u).
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Multiply -1 by -1.
-1(25-5u-5u+1uu)25-u
Multiply u by 1.
-1(25-5u-5u+uu)25-u
Raise u to the power of 1.
-1(25-5u-5u+u1u)25-u
Raise u to the power of 1.
-1(25-5u-5u+u1u1)25-u
Use the power rule aman=am+n to combine exponents.
-1(25-5u-5u+u1+1)25-u
Add 1 and 1.
-1(25-5u-5u+u2)25-u
-1(25-5u-5u+u2)25-u
Rewrite u2 as u.
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Use axn=axn to rewrite u as u12.
-1(25-5u-5u+(u12)2)25-u
Apply the power rule and multiply exponents, (am)n=amn.
-1(25-5u-5u+u12⋅2)25-u
Combine 12 and 2.
-1(25-5u-5u+u22)25-u
Cancel the common factor of 2.
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Cancel the common factor.
-1(25-5u-5u+u22)25-u
Divide 1 by 1.
-1(25-5u-5u+u1)25-u
-1(25-5u-5u+u1)25-u
Simplify.
-1(25-5u-5u+u)25-u
-1(25-5u-5u+u)25-u
-1(25-5u-5u+u)25-u
Subtract 5u from -5u.
-1(25-10u+u)25-u
-1(25-10u+u)25-u
Move the negative in front of the fraction.
-25-10u+u25-u
Simplify ( square root of u-5)/(5+ square root of u)

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