How do you multiply #1/(2x) + 3/(x+7) = -1/x#?

Question

Hazel Anglin · Accepted Answer

# (1/(2x)) + (3 /(x+7)) = -(1/x)#
# (1/(2x)) + (1/x)  = -(3 /(x+7))# # (1/(2x)) + ((1 xx 2)/(x xx 2))  = -(3 /(x+7))# L.C.M of the L.H.S is #2x# # (1/(2x)) + ((2)/(2x))  = -(3 /(x+7))# # 3/(2x) = -(3 /(x+7))# # 3/(2x) = (-3) /(x + 7)# on cross multiplying:
# 3 xx (x + 7)  = (-3) xx (2x)# # 3x + 21 = -6x# # 9x = -21# # x = -7/3#

Nathan Axel · Answer

undefined To solve the equation 1/(2x) + 3/(x+7) = -1/x, we need to find a common denominator and combine the fractions. The common denominator is 2x(x+7). Multiplying each term by the common denominator, we get (x+7) + 6x = -2(x+7). Simplifying, we have x + 7 + 6x = -2x - 14. Combining like terms, we get 7x + 7 = -2x - 14. Moving all the terms to one side, we have 7x + 2x = -14 - 7. Simplifying further, we get 9x = -21. Dividing both sides by 9, we find x = -21/9, which simplifies to x = -7/3. Therefore, the solution to the equation is x = -7/3.

Kennedy Adams · Answer

undefined To multiply the equation $ \frac{1}{2x} + \frac{3}{x+7} = -\frac{1}{x} $ by $ 2x(x + 7) $, you would multiply each term in the equation by $ 2x(x + 7) $. This step is taken to clear the denominators and simplify the equation.