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(3x+4y)/(6x^(2)y)-(3x-4y)/(6x^(2)y)

3x+4y6x2y−3x−4y6x2y \frac{3 x+4 y}{6 x^{2} y}-\frac{3 x-4 y}{6 x^{2} y}

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Full solution

Q. 3x+4y6x2y−3x−4y6x2y \frac{3 x+4 y}{6 x^{2} y}-\frac{3 x-4 y}{6 x^{2} y}
  1. Combine fractions: Combine the two fractions since they have the same denominator.\newline(3x+4y)/(6x2y)−(3x−4y)/(6x2y)=(3x+4y−(3x−4y))/(6x2y)(3x+4y)/(6x^{2}y) - (3x-4y)/(6x^{2}y) = (3x+4y - (3x-4y))/(6x^{2}y)
  2. Simplify numerator: Simplify the numerator by distributing the negative sign and combining like terms.\newline(3x+4y−3x+4y)/(6x2y)=(3x+4y−3x+4y)/(6x2y)(3x+4y - 3x + 4y)/(6x^{2}y) = (3x + 4y - 3x + 4y)/(6x^{2}y)
  3. Cancel terms: Cancel out the 3x3x terms and combine the 4y4y terms.\newline(0x+8y)/(6x2y)=8y/(6x2y)(0x + 8y)/(6x^{2}y) = 8y/(6x^{2}y)
  4. Reduce fraction: Simplify the fraction by reducing common factors.\newline8y6x2y=86yy1x2\frac{8y}{6x^{2}y} = \frac{8}{6}\frac{y}{y}\frac{1}{x^{2}}
  5. Final simplification: Reduce the fraction 86\frac{8}{6} to its simplest form and cancel out the yy terms.\newline43/x2=43x2\frac{4}{3}/x^{2} = \frac{4}{3x^{2}}

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