This faces adding, subtracting and finding the least prevalent multiple.
You are watching: 1:x = x:64. what one number can replace x
Step by Tip Solution
Rearrange:Reararray the equation by subtracting what is to the appropriate of the equal sign from both sides of the equation : 1/x-(x/64)=0
Tip by step solution :
Step 1 :
x Simplify —— 64Equation at the end of step 1 : 1 x — - —— = 0 x 64
Tip 2 :1 Simplify — xEquation at the finish of step 2 : 1 x — - —— = 0 x 64
Step 3 :Calculating the Leastern Common Multiple :3.1 Find the Least Common Multiple The left denominator is : x The best denominator is : 64
|Product of allPrime Factors||1||64||64|
Least Usual Multiple: 64xCalculating Multipliers :
3.2 Calculate multipliers for the two fractions Denote the Leastern Usual Multiple by L.C.M Denote the Left Multiplier by Left_M Denote the Right Multiplier by Right_M Denote the Left Deniminator by L_Deno Denote the Right Multiplier by R_DenoLeft_M=L.C.M/L_Deno=64Right_M=L.C.M/R_Deno=xMaking Equivalent Fractions :
3.3 Recompose the two fractions right into tantamount fractionsTwo fractions are referred to as indistinguishable if they have the same numeric value. For instance : 1/2 and 2/4 are identical, y/(y+1)2 and also (y2+y)/(y+1)3 are identical also. To calculate equivalent fraction , multiply the Numerator of each fractivity, by its corresponding Multiplier.
L. Mult. • L. Num. 64 —————————————————— = ——— L.C.M 64x R. Mult. • R. Num.
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x • x —————————————————— = ————— L.C.M 64x Adding fractions that have a prevalent denominator :3.4 Adding up the two identical fractions Add the two identical fractions which now have a widespread denominatorCombine the numerators together, put the sum or difference over the prevalent denominator then reduce to lowest terms if possible:
64 - (x • x) 64 - x2 ———————————— = ——————— 64x 64x Trying to element as a Difference of Squares:3.5 Factoring: 64 - x2 Theory : A difference of 2 perfect squares, A2-B2deserve to be factored right into (A+B)•(A-B)Proof:(A+B)•(A-B)= A2 - AB+BA-B2= A2 -AB+ AB - B2 = A2 - B2Keep in mind : AB = BA is the commutative property of multiplication. Note : -AB+ AB amounts to zero and is therefore got rid of from the expression.Check: 64 is the square of 8Check: x2 is the square of x1Factorization is :(8 + x)•(8 - x)Equation at the end of step 3 :
(x + 8) • (8 - x) ————————————————— = 0 64x
Tip 4 :When a fraction equates to zero :4.1 When a fraction equates to zero ...Where a portion equates to zero, its numerator, the part which is above the fractivity line, should equal zero.Now,to eliminate the denominator, Tiger multiplys both sides of the equation by the denominator.Here"s how:
(x+8)•(8-x) ——————————— • 64x = 0 • 64x 64x Now, on the left hand side, the 64x cancels out the denominator, while, on the right hand side, zero times anything is still zero.The equation now takes the shape:(x+8) • (8-x)=0
Theory - Roots of a product :4.2 A product of a number of terms equates to zero.When a product of 2 or even more terms amounts to zero, then at leastern among the terms should be zero.We shall currently resolve each term = 0 separatelyIn various other words, we are going to solve as many equations as there are terms in the productAny solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:4.3Solve:x+8 = 0Subtract 8 from both sides of the equation:x = -8
Solving a Single Variable Equation:4.4Solve:-x+8 = 0Subtract 8 from both sides of the equation:-x = -8 Multiply both sides of the equation by (-1) : x = 8