Simplify: (a) (6x2)/(x2-y2) − 3x/(x+y) + 3y/(y-x) (b) [(x+3x)2]/(x2-y2) × (x-y)/(x+3x)

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ScanSolve AI Tutor · Accepted Answer

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\frac{(x+3x)^2}{x^2-y^2} \times \frac{x-y}{x+3x}

Simplify the terms inside the parentheses.
$(x+3x)^2 = (4x)^2 = 16x^2$ $x+3x = 4x$
Substitute the simplified terms back into the expression.
$\frac{16x^2}{x^2-y^2} \times \frac{x-y}{4x}$
Factor the denominator $x^2-y^2$ using the difference of squares formula, $a^2-b^2 = (a-b)(a+b)$ .
$x^2-y^2 = (x-y)(x+y)$
Substitute the factored denominator into the expression.
$\frac{16x^2}{(x-y)(x+y)} \times \frac{x-y}{4x}$
Multiply the fractions and cancel out common factors $(x-y)$ and $4x$ .
$\frac{16x^2 (x-y)}{(x-y)(x+y) (4x)} = \frac{16x^2}{4x(x+y)}$
Simplify the remaining terms.
$\frac{16x^2}{4x(x+y)} = \frac{4x}{x+y}$
The simplified expression is $\boxed{\frac{4x}{x+y}}$ .

Simplify: (a) (6x2)/(x2-y2) - 3x/(x+y) + 3y/(y-x) (b) [(x+3x)2]/(x2-y2) * (x-y)/(x+3x)