If a-x-2y2x-y b-x-3y3x-y- then find the value of ab - 5a - b-

The correct option is B 1 [ = ab + 5( a ...

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Byju's Answer

Standard X

Mathematics

Rational Expression

If a=x+2y2x...

Question

If $a = \frac{x + 2 y}{2 x + y}$ & $b = \frac{x + 3 y}{3 x + y}$ , then find the value of ab + 5(a - b).

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Solution

The correct option is B $1$
$\begin{matrix} = a b + 5 (a - b) = (\frac{x + 2 y}{2 x + y}) (\frac{x + 3 y}{3 x + y}) + 5 (\frac{x + 2 y}{2 x + y} - \frac{x + 3 y}{3 x + y}) = \frac{x^{2} + 5 x y + 6 y^{2}}{(2 x + y) (3 x + y)} + 5 (\frac{(x + 2 y) (3 x + y) - (x + 3 y) (2 x + y)}{(2 x + y) (3 x + y)}) = \frac{(x^{2} + 5 x y + 6 y^{2}) + 5 (3 x^{2} + 7 x y + 2 y^{2} - 2 x^{2} - 7 x y - 3 y^{2})}{(2 x + y) (3 x + y)} = \frac{x^{2} + 5 x y + 6 y^{2} + 5 x^{2} - 5 y^{2}}{(2 x + y) (3 x + y)} = \frac{6 x^{2} + 5 x y + y^{2}}{6 x^{2} + 5 x y + y^{2}} = 1 \end{matrix}$

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If a=x+2y2x+y & b=x+3y3x+y, then find the value of ab + 5(a - b).

The correct option is B 1=ab+5(a−b)=(x+2y2x+y)(x+3y3x+y)+5(x+2y2x+y−x+3y3x+y)=x2+5xy+6y2(2x+y)(3x+y)+5((x+2y)(3x+y)−(x+3y)(2x+y)(2x+y)(3x+y))=(x2+5xy+6y2)+5(3x2+7xy+2y2−2x2−7xy−3y2)(2x+y)(3x+y)=x2+5xy+6y2+5x2−5y2(2x+y)(3x+y)=6x2+5xy+y26x2+5xy+y2=1

If $a = \frac{x + 2 y}{2 x + y}$ & $b = \frac{x + 3 y}{3 x + y}$ , then find the value of ab + 5(a - b).