Question

simplify
rt6/ rt2+rt3 + 3rt2/rt6+rt3 -
4rt3/rt6+rt2
​

Answer 1

6/3rt2 - 2rt3 = 6/[rt3 * rt3 * rt2 - rt2 * rt2 *rt3]

= 6/rt3*rt2(rt3 - rt2)

= rt6*rt6/rt6(rt3 - rt2) = rt6/(rt3 - rt2)

Now, rationalising the denominator:

rt6*(rt3+rt2)/(rt3-rt2)*(rt3+rt2)

= rt2*rt3(rt3 + rt2)/3-2

= 3rt2 + 2rt3

Hence, answer = 3*root2 + 2*root3.

Hope it helps.

[you can also rationalize the denominator using: 3rt2 + 2rt3 in the first step instead of the simplification process that i'd done]

Answer 2

Answer:

6/3rt2 - 2rt3 = 6/[rt3 * rt3 * rt2 - rt2 * rt2 *rt3]

= 6/rt3*rt2(rt3 - rt2)

= rt6*rt6/rt6(rt3 - rt2) = rt6/(rt3 - rt2)

Now, rationalising the denominator:

rt6*(rt3+rt2)/(rt3-rt2)*(rt3+rt2)

= rt2*rt3(rt3 + rt2)/3-2

= 3rt2 + 2rt3

Hence, answer = 3*root2 + 2*root3.

Hope it helps.

[you can also rationalize the denominator using: 3rt2 + 2rt3 in the first step instead of the simplification process that i'd done]

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hope it helps....

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