Question
A board of length Start Fraction 7 over x minus 2 End Fractionm was cut into two pieces. If one piece is Start Fraction 3 over x plus 2 End Fractionm, express the length of the other board, in meters, as a rational expression.
Answers
GPT 3.5
Let the length of the other board be y meters.
Since the total length of the board is Start Fraction 7 over x minus 2 End Fractionm, the sum of the lengths of the two pieces is the total length:
y + Start Fraction 3 over x plus 2 End Fractionm = Start Fraction 7 over x minus 2 End Fractionm
To find the length of the other board, we can isolate y on one side of the equation:
y = Start Fraction 7 over x minus 2 End Fractionm - Start Fraction 3 over x plus 2 End Fractionm
y = Start Fraction 7(x + 2) - 3(x - 2) over (x - 2)(x + 2)
y = Start Fraction 7x + 14 - 3x + 6 over (x - 2)(x + 2)
y = Start Fraction 4x + 20 over (x - 2)(x + 2)
Therefore, the length of the other board is given by the rational expression Start Fraction 4x + 20 over (x - 2)(x + 2) End Fractionm.
Since the total length of the board is Start Fraction 7 over x minus 2 End Fractionm, the sum of the lengths of the two pieces is the total length:
y + Start Fraction 3 over x plus 2 End Fractionm = Start Fraction 7 over x minus 2 End Fractionm
To find the length of the other board, we can isolate y on one side of the equation:
y = Start Fraction 7 over x minus 2 End Fractionm - Start Fraction 3 over x plus 2 End Fractionm
y = Start Fraction 7(x + 2) - 3(x - 2) over (x - 2)(x + 2)
y = Start Fraction 7x + 14 - 3x + 6 over (x - 2)(x + 2)
y = Start Fraction 4x + 20 over (x - 2)(x + 2)
Therefore, the length of the other board is given by the rational expression Start Fraction 4x + 20 over (x - 2)(x + 2) End Fractionm.