i need help solving these equations?

Question

1) x-3 / 10 = 4/5

2) 3/x +4 = 3/x

and expressing these in lowest terms:

x^2 - 5x / x^2 multiplied by x/ 2x-10

x^2 - 25 / 12 divide x^2 - 10x +25 / 4

(x^2 - 5x) / (x^2) multiplied by (x) / (2x-10)

(x^2 - 25) / (12) divide (x^2 - 10x +25) / 4

Answer 1

1) multiply both sides by 10:
(x-3) = 8
x = 11


2) cross multiply:
3/(x+4) = 3/x
3x = 3(x+4)

divide by 3:
x = x+4
0= 4

since this is NOT true, there is no solution



3) (x^2 - 5x) / (x^2) *(x)/ (2x-10)

multiply across:
(x^2 - 5x)(x) / (x^2)(2x-10)

there are 2 ways you could go, either multiply the parentheses or you could factor and cancel:

i) x^3- 5x^2 / 2x^3 - 10x^2
x^2(x-5)/2x^2(x-5)

=1/2

ii) x(x - 5)(x) / 2(x^2)(x-5)
x^2(x-5) / 2x^2(x-5)

same thing happens:
=1/2



4) ((x^2 - 25) / 12) / ((x^2 - 10x +25) / 4)

dividing fractions is like multiplying by the reciprocal:

((x^2 - 25) / 12) * (4/(x^2 - 10x +25)

you can cancel now:
((x^2 - 25) / 3) * (1/(x^2 - 10x +25)

now factor:
[(x-5)(x+5) / 3] *[1/(x-5)(x-5)]

= (x+5)/3(x-5)

Answer 2

x-3/10=4/5
Multiply both sides by 10
x-3=8
x=11

3/x + 4=3/x
Subtract 3/x from both sides
4=0, which is impossible
This equation is invalid.

x^2-5x /x^2 X x/2x-10
x(x-5)/x^2 X x/2(x-5)
x(x-5)x /2x^2(x-5)
x^2(x-5) / 2x^2(x-5)
1/2

(x^2-25)/12 / (x^2-10x+25)/4
(x^2-25)/12 X 4/(x^2-10x+25)
(x+5)(x-5)/12 X 4/(x-5)(x-5)
4(x+5)(x-5) / 12(x-5)(x-5)
(x+5)/3(x-5)

Answer 3

Most of these are just a matter of knowing how to "clean up" equations.

1, Multiply both sides by 10
2. As shown, the equation is not correct. If the denom. on the left is (x+4), then you can cross-multiply and solve.
3. Note that x^2-5x and 2x-10, when factored, will leave you with a common factor which can be cancelled out.
4. When you divide, you just "flip" the second term over. Again x^2-25 is the sum and difference of terms, and one of these terms, when squared gives you the quadratic on the right.

Answer 4

1) (x-3)/10 = 4/5
x-3=40/5=8
x=11

2) Undefined....since 3/x+4=3/x-------->4=0

Answer 5

1.) 10(4) = 5x-15 after you cross multiply
40+15= 5x
x=11

2.)(4x+3)/x=3/x
3x=4x/\2 + 3x
undefined

and for the last ones you need to put parenthesis in certain places to have enough information to simplify them