One number is 5 times another. Write an expression for the sum of their reciprocals. Then simplify the expression. (Use x for the variable.)
Solve the following equation. Be sure to check each answer in the original equation if you multiply both sides by an expression that contains a variable.
2/y+5+4/y−2= −2/y2+3y−10
thank you!
GunsUpTech
First number is x; second number is 5x. Reciprocal of 1st is 1/x; reciprocal of second is 1/(5x):
1/x + 1/(5x)
Get a common denominator by multiplying the first term by 5/5:
5/(5x) + 1/(5x)
Add the numerators
6/(5x)<====ANSWER
Multiply everything by the common denominator of (y^2 + 3y - 10), which is the same thing as (y + 5)(y - 2):
2(y + 5)(y - 2)/(y + 5) + 4(y + 5)(y - 2)/(y - 2) = -2(y^2 + 3y - 10)/(y^2 + 3y - 10)
2(y - 2) + 4(y + 5) = -2
2y - 4 + 4y + 20 = -2
6y + 16 = -2
6y = -18
y = -3<===ANSWER
Check by plugging -3 in for y in the original:
2/(-3 + 5) + 4(-3 - 2) = -2/(-3^2 + 3(-3) - 10)
2/2 + 4/-5 = -2/(-10)
1 - 4/5 = 1/5
1/5 = 1/5
?
1/x + 1/(5x) = 6/(5x)
Use parentheses to clarify the second problem and a caret, ^, to indicate exponents