# maths (exponents

if abc=1 prove that 1/(1+a+b^-1) + 1/(1+b+c^-1) +1/(1+c+a^-1) =1

1. 👍 0
2. 👎 0
3. 👁 112
1. Well, just using brute force, we have

b/(b+ab+1) + c/(c+bc+1) + a/(a+ac+1)

expand all that over a common denominator, and you get

(a^2b^2c + a^bc^2 + 2a^2bc + a^2b + ab^2c^2 + 2ab^2c + 2abc^2 + 6abc + 2ab + ac^2 + 2ac + a + b^2c + 2bc + b + c)
/
(a^2b^2c^2 + a^2b^2c + a^2bc^2 + 2a^2bc + a^2b + ab^2c^2 + 2ab^2c + 2abc^2 + 4abc + 2ab + ac^2 + 2ac + a + b^2c + 2bc + b + c + 1)

now replace all the abc occurrences with just 1, and you have

(ab + ac + 2a + a^2b + bc + 2b + 2c + 6 + 2ab + ac^2 + 2ac + a + b^2c + 2bc + b + c)
/
(ab + ac + 2a + a^2b + bc + 2b + 2c + 6 + 2ab + ac^2 + 2ac + a + b^2c + 2bc + b + c)

where the top and bottom are clearly the same.

Now, for a trick of evaluation which avoids all that mess, I haven't come up with one yet.

1. 👍 0
2. 👎 0
posted by Steve

## Similar Questions

1. ### Math Geometry

Geometry Question: Prove the symmetric Property for congruence of triangles. Given: ∆ABC≅ ∆DEF Prove: ∆DEF≅ ∆ABC

asked by Reigel on May 18, 2011
2. ### Math- any help would be greatly appreciated

In triangle ABC, the medians AD,BE, and CF concur at the centroid G. (a) Prove that AD < (AB + AC)/2. (b) Let P=AB+AC+BC be the perimeter of triangle ABC. Prove that 3P/4 < AD + BE + CF < P.

asked by Stephanie on May 19, 2016
3. ### Math

In triangle ABC, the medians AD,BE, and CF concur at the centroid G. (a) Prove that AD < (AB + AC)/2. (b) Let P=AB+AC+BC be the perimeter of triangle ABC. Prove that 3P/4 < AD + BE + CF < P.

asked by Stephanie on May 19, 2016
4. ### Geometry

Given: ∠ABC and ∠CBD are supplementary angles. m∠ABC = 4x + 7, m∠CBD = 2x − 1. Prove: m∠ABC = 123 How do I write this in a two column proof?

asked by Kate on September 30, 2017
5. ### Math

Suppose line GH is congruent to line JK, line HE is congruent to line KL, and angle 1 is congruent to angle L. Can you prove that triangle GHI is congrunet to triangke JKL, abd if so, how? A. You can use SAS to prove the triangles

asked by Bettey on October 8, 2018
1. ### Math

From the vertex A of a right angled triangle ABC, (A being the right angle) AD is drawn perpendicular to BC. How do I prove that the three triangles ABD, ADC, and ABC are similar? Thank you!

asked by Mintz on July 8, 2010
2. ### Advanced Maths (Vectors) AQA Level

Triangle ABC with D, E and F the midpoints of BC, AC, and AB. G is the midpoint of AD such that the ratio AG:GD =2:1, VECtors AB =p and BC =q Prove that B, G and E are collinear. prove the same results for point C, G and F

asked by Jat on February 12, 2012
3. ### Advanced Maths (Vectors) AQA Level

Triangle ABC with D, E and F the midpoints of BC, AC, and AB. G is the midpoint of AD such that the ratio AG:GD =2:1, VECtors AB =p and BC =q Prove that B, G and E are collinear. prove the same results for point C, G and G

asked by Jat on February 12, 2012
4. ### Geometry..

Given: A(3,-1), B(5,2), C(-2,0), P(-3,4), Q(-5,-3), R(-6,2). Prove: angles ABC and RPQ are congruent by completing the paragraph proof. AB=RP=13, BC=(?)=53, and CA=QR=26. So segment AB is congruent to (?), segments BC and PQ are

asked by Wendell on July 26, 2011
5. ### Geometry.

prove that the distance between any two points inside triangle abc is not greater than half the perimeter of triangle abc my teacher said to try doing this proof by contradiction. can someone please help??

asked by Sammy on December 19, 2013
6. ### Geometry

∠ABC and ∠ABD are a linear pair. Prove that m∠ABC + m∠ABD = 180°. Write a paragraph proof

asked by Kathy on September 30, 2017

More Similar Questions