Simplify (7√3)/(√10 + √3)−(2√5)/(√6 + √5)−(3√2)/(√15 + 3√2)

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Simplify (7√3)/(√10 + √3)−(2√5)/(√6 + √5)−(3√2)/(√15 + 3√2) We solve them separately (𝟕√𝟑)/(√𝟏𝟎 + √𝟑) = (7√3)/(√10 + √3) × (√10 − √3)/(√10 − √3) = (7√3(√10 − √3))/((√10)^2− (√3)^2 ) = (7√3(√10 − √3))/7 (𝟐√𝟓)/(√𝟔 + √𝟓) = (2√5)/(√6 + √5) × (√6 − √5)/(√6 − √5) = (2√5(√6 − √5))/((√6)^2− (√5)^2 ) = (2√5(√6 − √5))/1 = 2√5(√6 − √5) = 𝟐√𝟑𝟎−𝟏𝟎 (𝟑√𝟐)/(√𝟏𝟓 + 𝟑√𝟐) = (3√2)/(√15 + 3√2) × (√15 − 3√2)/(√15 − 3√2) = (3√2(√15 − 3√2))/((√15)^2− (3√2)^2 ) = (3√2(√15 − 3√2))/(15 − 9 × 2) = (3√2(√15 − 3√2))/(−3) = −√2(√15 − 3√2) Now, (𝟕√𝟑)/(√𝟏𝟎 + √𝟑)−(𝟐√𝟓)/(√𝟔 + √𝟓)−(𝟑√𝟐)/(√𝟏𝟓 + 𝟑√𝟐) = (√30−3)−(2√30−10)−(−√30+6) = √30−3−2√30+10+√30−6 = (√30−2√30+√30)+(−3+10−6) = 𝟏