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How do you solve #7/(x+2)= 2/(x-5)#?

Answer 1

#x=39/5=7 4/5#

Given #color(white)("XXX")7/(x+2)=2/(x-5)color(white)("XXX")#note: this equation implies #x!=-2# and #x!=5#

Multiply both sides by #(x+2)(x-5)# (sometimes this will be called "cross multiplying") #color(white)("XXX")7(x-5)=2(x+2)# simplify: #color(white)("XXX")7x-35=2x+4# subtract #2x# from both sides and add #35# to both sides #color(white)("XXX")5x=39# divide both sides by #5# #color(white)("XXX")x=39/5#

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Answer 2

Jace Anderson

To solve the equation ( \frac{7}{x+2} = \frac{2}{x-5} ), you can cross-multiply to eliminate the denominators. This gives:

[ 7(x - 5) = 2(x + 2) ]

Expanding both sides:

[ 7x - 35 = 2x + 4 ]

Next, collect like terms:

[ 7x - 2x = 35 + 4 ]

[ 5x = 39 ]

Divide both sides by 5 to solve for ( x ):

[ x = \frac{39}{5} ]

Therefore, the solution is ( x = \frac{39}{5} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.