Algebra Help again?

Question

1) -3a^2b/35a^5 * 14a^3b^2/-9b^4 (multiply)
2)y-2/y+3 subtract y/2y + 6
3)x/7 + 10 = 9 (is this answer -7?)

Thanks for your help!

Answer 1

1. First: combine the numerators & denominators.

[(-3a^2b)(14a^3b^2)]/[(35a^5)(-9b^4)]

*When you multiply the same variables - add exponents.

(- 42a^5b^3)/(- 315a^5b^4)
(42a^5b^3)/(315a^5b^4)

*Simplify the coefficients > 42/315 = 2/15

(2a^5b^3)/(15a^5b^4)

Sec: simplify the "a" variables - when you divide the same variables, subtract exponents...

a^(5-5) = a^0 = 1

Now you have > (2b^3)/(15b^4)

*Simplify the "b" variables > b^(3 - 4) = b^-1

Now you have >>> (2b^-1)/15

Third: rule - the variable has to have a positive exponent > place the variable in the denominator....

= 2/(15b)

2. (y-2/y+3) - (y/2y+6)

*Factor the denominator in the 2nd fraction....

(y-2/y+3) - [y/2(y+3)]

*Find the greatest common denominator which is, 2(y+3)..

First: multiply the fractions with the missing values to get the greatest common denominator....

(2)(y-2/y+3) - [y/2(y+3)]
[2(y-2)/2(y+3)] - [y/2(y+3)]
[2(y)+2(-2)/2(y)+2(3)] - [y/2(y+3)]
[2y-4/2y+6)] - [y/2y+6)]

Sec: combine the numerators & place them over the denominator....

(2y - 4 - y)/(2y+6)
(y - 4)/(2y+6)

3. Yes - the solution is -7.

Answer 2

1) -3a^2b/35a^5 * 14a^3b^2/-9b^4 (multiply)
= -42a^5b^3/-315a5b^4 = 2/15b

2)y-2/y+3 subtract y/2y + 6 = (y-2)/(y+3)-y/(2(y+3))
=2(y-2)/2(y+3)) - y/(2(y+3)) = (2y-4-y)/2(y+3) =( y-4)/(2(y+3)


3)x/7 + 10 = 9 (is this answer -7?)
x/7 =9 - 10 = -1
x = -7 Correct you are

Answer 3

1) -3a²b/35a^5 * 14a³b²/-9b^4 (multiply)
multiplying numerators: (-3 x 14)(a²ba³b²) = -42a^5b^5
multplying denominators: (35 x -9)(a^5b^4) = -315a^5b^4
Dividing denominator by numerator
-42a^5b^5 / -315a^5b^4 = (-42:-315)and(a^5b^5 ; a^5b^4) =
2/15 and (a^5:a^5)(b^5:b^4) = 2/15(1)(b) = 2/15b
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2)y-2/y+3 subtract y/2y + 6
(y-2/y+3) - (y/2y + 6)
lcf(y+3 and 2y + 6) = 2y + 6 or 2(y + 3)
2(y - 2) - y = 2y - 4 -y =
y - 4 => y = 4
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3)x/7 + 10 = 9
70 + x = 63
x = 63 - 70
x = -7
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Answer 4

1) -3a^2b (14a^3b^2) / 35a^5 ( -9b^4) Mult or cancel

-3(14)a^5b^3 / 35(-9)a^5b^4

2 / 15 b

2) y - 2 / y+3 - y / 2(y+3) common den = 2(y+3)


2(y-2) - y / 2(y+3) = 2y - 4 - y /2(y + 3) =

y - 4 / 2(y + 3)

3) x/7 = -1

x = -7