simplify: 1/1+x b-a +xc-a + 1/1+x b-a +xc-a +1/1+x b-a +xc-a
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1/(1 + xᵇ⁻ᵃ + xᶜ⁻ᵃ) + 1/(1 + xᵃ⁻ᵇ + xᶜ⁻ᵇ) + 1/(1 + xᵇ⁻ᶜ + xᵃ⁻ᶜ) = 1
Step-by-step explanation:
L.H.S. = 1/(1 + xᵇ⁻ᵃ + xᶜ⁻ᵃ) + 1/(1 + xᵃ⁻ᵇ + xᶜ⁻ᵇ) + 1/(1 + xᵇ⁻ᶜ + xᵃ⁻ᶜ)
= 1/(1 + xᵇ/xᵃ + xᶜ/xᵃ) + 1/(1 + xᵃ/xᵇ + xᶜ/xᵇ) + 1/(1 + xᵇ/xᶜ + xᵃ/xᶜ)
= 1/{(xᵃ + xᵇ + xᶜ)/xᵃ} + 1/{(xᵇ + xᵃ + xᶜ)/xᵇ} + 1/{(xᶜ + xᵇ + xᵃ)/xᶜ}
= xᵃ/(xᵃ + xᵇ + xᶜ) + xᵇ/(xᵃ + xᵇ + xᶜ) + xᶜ/(xᵃ + xᵇ + xᶜ)
= (xᵃ + xᵇ + xᶜ)/(xᵃ + xᵇ + xᶜ)
= 1 = R.H.S.
Hence, proved.
Rule:
xᵃ⁻ᵇ = xᵃ * x⁻ᵇ = xᵃ * 1/xᵇ = xᵃ/xᵇ
Step-by-step explanation:
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