divide rationalize the binomial denominator express answer w

divide, rationalize the binomial denominator. express answer with radicals

squareroot 5 c+ 3d/squareroot 5c - d divide, rationalize the binomial denominator. express answer with radicals

Solution

(sqrt(5c) +3d )/( sqrt(5c) - d)

rationalise denominator by multiplying the denominator and numerator by sqrt(5c) +d

(sqrt(5c) +3d )( sqrt(5c) -d)/(( sqrt(5c) - d)( sqrt(5c) +d)

= (5c - d*sqrt(5c) + 3d*sqrt(5c) -3d^2 )/( 5c - d^2)

= (5c +2dsqrt(5c) -3d^2)/(5c -d^2)